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Venn Diagram - Interactive

Venn Diagram - Interactive
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2020-07-22 00:35
Geometric ConstructionSlider Animation
This example demonstrates interactive Venn diagrams, involving core concepts of set theory. Using GeoGebra commands such as Polygon, Intersect, Circle, and Point, you can construct intersections, unions, and complements of two or three sets. Suitable for middle school and above students to learn basic set operations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Intersect(a, d) → E
  3. Intersect(a, b) → F
  4. Intersect(b, c) → G
  5. Intersect(c, d) → H
  6. Polygon(E, F, G, H) → q2, e, f, g, h
  7. Circle(I, 2) → k
  8. Circle(J, 2) → p
  9. Circle(K, 1.97) → q
  10. Circle(L, 1.97) → r
  11. Circle(M, 1.97) → s
  12. Circle(N, 1.97) → t
  13. Intersect(k, p, 2) → O
  14. Point(p) → P
  15. Point(p) → Q
  16. Point(p) → R
  17. Point(p) → S
  18. Point(p) → T
  19. Point(p) → U
  20. Point(p) → V
  21. Point(p) → W
  22. Intersect(k, p, 1) → Z
  23. Point(k) → A_1
  24. Point(k) → B_1
  25. Point(k) → C_1
  26. Point(k) → D_1
  27. Point(k) → E_1
  28. Point(k) → F_1
  29. Point(k) → G_1
  30. Point(k) → H_1
  31. Point(k) → I_1
  32. Point(k) → J_1
  33. Point(k) → K_1
  34. Point(k) → L_1
  35. Point(k) → M_1
  36. Point(k) → N_1
  37. Point(k) → O_1
  38. Point(k) → P_1
  39. Point(k) → Q_1
  40. Point(k) → R_1
  41. Point(k) → S_1
  42. Point(k) → T_1
  43. Point(k) → U_1
  44. Point(k) → V_1
  45. Point(k) → W_1
  46. Point(k) → Z_1
  47. Point(k) → A_2
  48. Point(k) → B_2
  49. Point(k) → C_2
  50. Point(k) → D_2
  51. Point(k) → E_2
  52. Polygon(O, P, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, Q, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, R, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, S, T, U, V, W, Z) → poly1, o, z_1, a_1, b_1, c_1, d_1, e_1, f_1, g_1, h_1, i_1, p_1, j_1, k_1, l_1, m_1, n_1, o_1, f_2, g_2, h_2, i_2, q_1, j_2, u_1, v_1, w_1, k_2, a_2, b_2, c_2, d_2, e_2, r_1, s_1, t_1, u, v, w
  53. Intersect(k, p, 2) → F_2
  54. Point(p) → G_2
  55. Point(p) → H_2
  56. Point(p) → I_2
  57. Point(p) → J_2
  58. Point(p) → K_2
  59. Point(p) → L_2
  60. Point(p) → M_2
  61. Point(p) → N_2
  62. Point(p) → O_2
  63. Point(p) → P_2
  64. Point(p) → Q_2
  65. Point(p) → R_2
  66. Point(p) → S_2
  67. Point(p) → T_2
  68. Point(p) → U_2
  69. Point(p) → V_2
  70. Point(p) → W_2
  71. Point(p) → Z_2
  72. Point(p) → A_3
  73. Point(p) → B_3
  74. Point(p) → C_3
  75. Point(p) → D_3
  76. Point(p) → E_3
  77. Point(p) → F_3
  78. Intersect(k, p, 1) → G_3
  79. Point(k) → H_3
  80. Point(k) → I_3
  81. Point(k) → J_3
  82. Point(k) → K_3
  83. Point(k) → L_3
  84. Point(k) → M_3
  85. Point(k) → N_3
  86. Point(k) → O_3
  87. Point(k) → P_3
  88. Point(k) → Q_3
  89. Polygon(F_2, G_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2, A_3, H_2, B_3, C_3, D_3, E_3, F_3, G_3, H_3, I_3, J_3, K_3, I_2, L_3, M_3, N_3, O_3, P_3, Q_3, J_2, K_2, L_2, M_2, N_2, O_2) → poly2, m_2, o_2, h_3, i_3, j_3, k_3, l_3, u_2, v_2, w_2, z_2, n_2, a_3, b_3, c_3, d_3, e_3, m_3, n_3, p_3, q_3, r_3, p_2, s_3, t_3, f_4, g_4, o_3, h_4, i_4, q_2, r_2, s_2, t_2, f_3, g_3
  90. Polygon(O, Q_3, H_3, Z, W, V, U, T, S, R, Q, P, P_3, O_3, N_3, M_3, L_3, K_3, J_3, I_3) → poly3, o_4, s_4, t_4, z_3, w_3, v_3, u_4, t_5, s_5, r_5, q_5, j_4, p_5, k_4, l_4, m_4, n_4, p_4, q_4, r_4
  91. Polygon(O, Q_3, H_3, Z, W, V, U, T, S, R, Q, P, P_3, O_3, N_3, M_3, L_3, K_3, J_3, I_3) → poly4, o_5, j_5, k_5, z_4, w_4, v_4, u_5, t_6, s_6, r_6, q_6, b_4, p_6, c_4, d_4, e_4, f_5, g_5, h_5, i_5
  92. Circle(R_3, 2) → c_5
  93. Circle(S_3, 1.97) → d_5
  94. Intersect(k, c_5, 2) → T_3
  95. Point(c_5) → U_3
  96. Point(c_5) → V_3
  97. Point(c_5) → W_3
  98. Point(c_5) → Z_3
  99. Intersect(k, c_5, 1) → A_4
  100. Point(k) → B_4
  101. Point(k) → C_4
  102. Point(k) → D_4
  103. Point(k) → E_4
  104. Point(k) → F_4
  105. Point(k) → G_4
  106. Point(k) → H_4
  107. Point(k) → I_4
  108. Point(k) → J_4
  109. Point(k) → K_4
  110. Point(k) → L_4
  111. Point(k) → M_4
  112. Point(k) → N_4
  113. Point(k) → O_4
  114. Point(k) → P_4
  115. Polygon(T_3, U_3, F_4, G_4, H_4, I_4, J_4, K_4, L_4, M_4, N_4, O_4, V_3, P_4, W_3, Z_3, A_4, B_4, C_4, D_4, E_4) → poly5, l_5, k_6, l_6, m_6, n_6, a_6, b_6, c_6, d_6, e_6, f_7, m_5, g_7, h_7, n_5, e_5, f_6, g_6, h_6, i_6, j_6
  116. Intersect(k, c_5, 2) → Q_4
  117. Point(k) → R_4
  118. Point(k) → S_4
  119. Point(k) → T_4
  120. Point(k) → U_4
  121. Point(k) → V_4
  122. Point(k) → W_4
  123. Intersect(k, c_5, 1) → Z_4
  124. Point(c_5) → A_5
  125. Point(c_5) → B_5
  126. Point(c_5) → C_5
  127. Point(c_5) → D_5
  128. Point(c_5) → E_5
  129. Point(c_5) → F_5
  130. Point(c_5) → G_5
  131. Point(c_5) → H_5
  132. Point(c_5) → I_5
  133. Point(c_5) → J_5
  134. Point(c_5) → K_5
  135. Point(c_5) → L_5
  136. Point(c_5) → M_5
  137. Point(c_5) → N_5
  138. Point(c_5) → O_5
  139. Point(c_5) → P_5
  140. Point(c_5) → Q_5
  141. Polygon(Q_4, R_4, C_5, D_5, E_5, F_5, G_5, H_5, I_5, J_5, K_5, L_5, S_4, M_5, N_5, O_5, P_5, Q_5, T_4, U_4, V_4, W_4, Z_4, A_5, B_5) → poly6, i_7, s_7, t_7, a_7, b_7, c_7, d_7, e_7, f_8, g_8, h_8, j_7, i_8, j_8, k_8, l_8, m_8, n_8, k_7, l_7, m_7, n_7, p_7, q_7, r_7
  142. Intersect(p, c_5, 2) → R_5
  143. Point(p) → S_5
  144. Point(p) → T_5
  145. Point(p) → U_5
  146. Point(p) → V_5
  147. Point(p) → W_5
  148. Point(p) → Z_5
  149. Point(p) → A_6
  150. Point(p) → B_6
  151. Point(p) → C_6
  152. Intersect(p, c_5, 1) → D_6
  153. Point(c_5) → E_6
  154. Point(c_5) → G_6
  155. Point(c_5) → H_6
  156. Point(c_5) → I_6
  157. Point(c_5) → J_6
  158. Point(c_5) → K_6
  159. Point(c_5) → L_6
  160. Point(c_5) → M_6
  161. Point(c_5) → N_6
  162. Point(c_5) → O_6
  163. Point(c_5) → P_6
  164. Point(c_5) → Q_6
  165. Point(c_5) → R_6
  166. Point(c_5) → S_6
  167. Point(c_5) → T_6
  168. Point(c_5) → U_6
  169. Point(c_5) → V_6
  170. Point(c_5) → W_6
  171. Point(c_5) → Z_6
  172. Point(c_5) → A_7
  173. Point(c_5) → B_7
  174. Polygon(R_5, S_5, D_6, E_6, F_6, G_6, H_6, I_6, J_6, K_6, L_6, M_6, T_5, N_6, O_6, P_6, Q_6, R_6, S_6, T_6, U_6, V_6, W_6, U_5, Z_6, A_7, B_7, V_5, W_5, Z_5, A_6, B_6, C_6) → poly7, p_8, d_8, e_8, f_9, g_9, h_9, i_9, j_9, k_9, l_9, m_9, q_8, n_9, p_9, o_6, q_9, r_9, s_9, t_9, a_9, u_6, v_6, r_8, w_6, z_6, b_9, c_9, s_8, t_8, a_8, z_5, b_8, c_8
  175. Intersect(p, c_5, 2) → C_7
  176. Point(c_5) → D_7
  177. Point(c_5) → E_7
  178. Point(c_5) → F_7
  179. Point(c_5) → G_7
  180. Point(c_5) → H_7
  181. Point(c_5) → I_7
  182. Intersect(p, c_5, 1) → J_7
  183. Point(p) → K_7
  184. Point(p) → L_7
  185. Point(p) → M_7
  186. Point(p) → N_7
  187. Point(p) → O_7
  188. Point(p) → P_7
  189. Point(p) → Q_7
  190. Point(p) → R_7
  191. Point(p) → S_7
  192. Point(p) → T_7
  193. Point(p) → U_7
  194. Point(p) → V_7
  195. Point(p) → W_7
  196. Point(p) → Z_7
  197. Point(p) → A_8
  198. Intersect(k, p, 1) → B_8
  199. Point(p) → C_8
  200. Point(p) → D_8
  201. Point(p) → E_8
  202. Polygon(C_7, D_7, M_7, N_7, O_7, P_7, Q_7, R_7, S_7, T_7, U_7, V_7, E_7, W_7, Z_7, A_8, B_8, C_8, D_8, E_8, F_7, G_7, H_7, I_7, J_7, K_7, L_7) → poly8, d_9, m_{10}, n_{10}, p_{10}, q_{10}, r_{10}, s_{10}, t_{10}, a_{10}, b_{10}, u_7, e_9, v_7, w_7, z_7, c_{10}, d_{10}, e_{10}, f_{11}, g_{11}, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}
  203. Intersect(p, c_5, 2) → F_8
  204. Point(p) → G_8
  205. Point(p) → H_8
  206. Point(p) → I_8
  207. Intersect(k, p, 1) → J_8
  208. Point(k) → K_8
  209. Point(k) → L_8
  210. Point(k) → M_8
  211. Point(k) → N_8
  212. Point(k) → O_8
  213. Point(k) → P_8
  214. Point(k) → Q_8
  215. Point(k) → R_8
  216. Point(k) → S_8
  217. Point(k) → T_8
  218. Point(k) → U_8
  219. Point(k) → V_8
  220. Point(k) → W_8
  221. Point(k) → Z_8
  222. Point(k) → A_9
  223. Intersect(k, c_5, 2) → B_9
  224. Point(c_5) → C_9
  225. Point(c_5) → D_9
  226. Point(c_5) → E_9
  227. Point(c_5) → F_9
  228. Polygon(F_8, G_8, P_8, Q_8, R_8, S_8, T_8, U_8, V_8, W_8, Z_8, A_9, H_8, B_9, C_9, D_9, E_9, F_9, I_8, J_8, K_8, L_8, M_8, N_8, O_8) → poly9, h_{11}, r_{11}, s_{11}, t_{11}, a_{11}, b_{11}, c_{11}, u_8, v_8, w_8, z_8, i_{11}, d_{11}, e_{11}, f_{12}, g_{12}, h_{12}, i_{12}, j_{11}, k_{11}, l_{11}, m_{11}, n_{11}, p_{11}, q_{11}
  229. Intersect(p, c_5, 1) → G_9
  230. Point(c_5) → H_9
  231. Point(c_5) → I_9
  232. Point(c_5) → J_9
  233. Point(c_5) → K_9
  234. Intersect(k, c_5, 1) → L_9
  235. Point(k) → M_9
  236. Point(k) → N_9
  237. Point(k) → O_9
  238. Intersect(k, p, 1) → P_9
  239. Point(p) → Q_9
  240. Point(p) → R_9
  241. Point(p) → S_9
  242. Point(p) → T_9
  243. Point(p) → U_9
  244. Point(p) → V_9
  245. Point(p) → W_9
  246. Point(p) → Z_9
  247. Point(p) → A_{10}
  248. Point(p) → B_{10}
  249. Point(p) → C_{10}
  250. Point(p) → D_{10}
  251. Polygon(G_9, H_9, Q_9, R_9, S_9, T_9, U_9, V_9, W_9, Z_9, A_{10}, B_{10}, I_9, C_{10}, D_{10}, J_9, K_9, L_9, M_9, N_9, O_9, P_9) → poly10, j_{12}, t_{12}, a_{12}, b_{12}, c_{12}, d_{12}, u_9, v_9, w_9, z_9, e_{12}, k_{12}, f_{13}, g_{13}, h_{13}, l_{12}, m_{12}, n_{12}, p_{12}, q_{12}, r_{12}, s_{12}
  252. Intersect(p, c_5, 1) → E_{10}
  253. Point(p) → F_{10}
  254. Point(p) → G_{10}
  255. Point(p) → H_{10}
  256. Point(p) → I_{10}
  257. Point(p) → J_{10}
  258. Intersect(k, p, 2) → K_{10}
  259. Point(k) → L_{10}
  260. Point(k) → M_{10}
  261. Point(k) → N_{10}
  262. Point(k) → O_{10}
  263. Point(k) → P_{10}
  264. Intersect(k, c_5, 2) → Q_{10}
  265. Point(c_5) → R_{10}
  266. Point(c_5) → S_{10}
  267. Point(c_5) → T_{10}
  268. Point(c_5) → U_{10}
  269. Point(c_5) → W_{10}
  270. Point(c_5) → Z_{10}
  271. Point(c_5) → A_{11}
  272. Point(c_5) → B_{11}
  273. Point(c_5) → C_{11}
  274. Point(c_5) → D_{11}
  275. Point(c_5) → E_{11}
  276. Point(c_5) → F_{11}
  277. Point(c_5) → G_{11}
  278. Point(c_5) → H_{11}
  279. Point(c_5) → I_{11}
  280. Point(c_5) → J_{11}
  281. Point(c_5) → K_{11}
  282. Polygon(E_{10}, F_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}, V_{10}, W_{10}, Z_{10}, G_{10}, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, J_{11}, H_{10}, K_{11}, I_{10}, J_{10}, K_{10}, L_{10}, M_{10}, N_{10}) → poly11, i_{13}, s_{13}, t_{13}, a_{13}, b_{13}, c_{13}, d_{13}, e_{13}, u_{10}, v_{10}, w_{10}, j_{13}, z_{10}, f_{14}, g_{14}, h_{14}, i_{14}, j_{14}, k_{14}, l_{14}, m_{14}, n_{14}, k_{13}, p_{14}, q_{14}, l_{13}, m_{13}, n_{13}, p_{13}, q_{13}, r_{13}
  283. Intersect(k, c_5, 2) → L_{11}
  284. Point(c_5) → M_{11}
  285. Point(c_5) → N_{11}
  286. Point(c_5) → O_{11}
  287. Point(c_5) → P_{11}
  288. Intersect(k, c_5, 1) → Q_{11}
  289. Point(k) → R_{11}
  290. Intersect(k, p, 2) → S_{11}
  291. Point(k) → T_{11}
  292. Point(k) → U_{11}
  293. Point(k) → V_{11}
  294. Point(k) → W_{11}
  295. Polygon(L_{11}, M_{11}, V_{11}, W_{11}, N_{11}, O_{11}, P_{11}, Q_{11}, R_{11}, S_{11}, T_{11}, U_{11}) → poly12, r_{14}, u_{11}, v_{11}, w_{11}, s_{14}, t_{14}, a_{14}, b_{14}, c_{14}, d_{14}, e_{14}, f_{15}
  296. Intersect(p, c_5, 2) → Z_{11}
  297. Point(p) → A_{12}
  298. Point(p) → B_{12}
  299. Point(p) → C_{12}
  300. Point(p) → D_{12}
  301. Point(p) → E_{12}
  302. Point(p) → F_{12}
  303. Intersect(p, c_5, 1) → G_{12}
  304. Point(c_5) → H_{12}
  305. Point(c_5) → I_{12}
  306. Point(c_5) → J_{12}
  307. Point(c_5) → K_{12}
  308. Point(c_5) → L_{12}
  309. Point(c_5) → M_{12}
  310. Point(c_5) → N_{12}
  311. Polygon(Z_{11}, A_{12}, J_{12}, K_{12}, L_{12}, M_{12}, N_{12}, B_{12}, C_{12}, D_{12}, E_{12}, F_{12}, G_{12}, H_{12}, I_{12}) → poly13, z_{11}, p_{15}, q_{15}, r_{15}, s_{15}, t_{15}, a_{15}, g_{15}, h_{15}, i_{15}, j_{15}, k_{15}, l_{15}, m_{15}, n_{15}
  312. Intersect(p, c_5, 2) → O_{12}
  313. Point(c_5) → P_{12}
  314. Point(c_5) → Q_{12}
  315. Intersect(k, c_5, 1) → R_{12}
  316. Point(k) → S_{12}
  317. Point(k) → T_{12}
  318. Point(k) → U_{12}
  319. Intersect(k, p, 2) → V_{12}
  320. Point(p) → W_{12}
  321. Point(p) → Z_{12}
  322. Point(p) → A_{13}
  323. Point(p) → B_{13}
  324. Polygon(O_{12}, P_{12}, A_{13}, B_{13}, Q_{12}, R_{12}, S_{12}, T_{12}, U_{12}, V_{12}, W_{12}, Z_{12}) → poly14, b_{15}, z_{12}, i_{16}, j_{16}, c_{15}, d_{15}, e_{15}, f_{16}, g_{16}, h_{16}, v_{12}, w_{12}
  325. Circle(C_{13}, 1.98) → c_{16}