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(C) Let the three sets of students playing the three games be $A$,$B$,and $C$.According to the problem,some students play two games,which means the in

Vedclass · Accepted Answer

None of these

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(C) Let the three sets of students playing the three games be $A$,$B$,and $C$.According to the problem,some students play two games,which means the intersection of any two sets is non-empty (i.e.,$A \cap B 
eq \emptyset$,$B \cap C 
eq \emptyset$,$A \cap C 
eq \emptyset$).However,no student plays all three games,which means the intersection of all three sets must be empty (i.e.,$A \cap B \cap C = \emptyset$).In diagram $P$,there are only two sets,so it does not represent three games.In diagram $Q$,the three circles are arranged such that there is a central region where all three overlap,meaning $A \cap B \cap C 
eq \emptyset$.In diagram $R$,the three circles are arranged such that there is no common region shared by all three circles,meaning $A \cap B \cap C = \emptyset$,while pairs of circles still overlap.Therefore,only diagram $R$ justifies the statement. Since $R$ is not present in any of the options $A$,$B$,or $D$,the correct option is $C$.

In a school,there are three types of games to be played. Some students play two types of games,but none play all three games. Which Venn diagram$(s)$ can justify the above statement?

Similar Questions

If $A=\{1, 2, 3, 4\}, B=\{3, 4, 5, 6\}, C=\{5, 6, 7, 8\}$ and $D=\{7, 8, 9, 10\}$,find $A \cup C$.

If $A = \{3, 6, 9, 12, 15, 18, 21\}, B = \{4, 8, 12, 16, 20\}, C = \{2, 4, 6, 8, 10, 12, 14, 16\}, D = \{5, 10, 15, 20\};$ find $D - C$.

If $A = \{3, 5, 7, 9, 11\}$,$B = \{7, 9, 11, 13\}$,$C = \{11, 13, 15\}$,and $D = \{15, 17\}$,find $(A \cap B) \cap (B \cup C)$.

Consider the following relations:
$(1) \, A - B = A - (A \cap B)$
$(2) \, A = (A \cap B) \cup (A - B)$
$(3) \, A - (B \cup C) = (A - B) \cup (A - C)$
Which of these is/are correct?

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