Let A, B and C be sets such that ϕ≠A∩B⊆C.Then which of the following statements is not true?
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a
B∩C≠ϕ
b
If (A−B)⊆C,thenA⊆C
c
(C∪A)∩(C∪B)=C
d
If (A−C)⊆B,then A⊆B
answer is D.
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Detailed Solution
According to the question, we have the following Venn diagram. Here, A∩B⊆C and A∩B≠ϕNow, from the Venn diagram, it is clear thatB∩C≠ϕ is true,Also,(C∪A)∩(C∪B)=C∪(A∩B)=C is trueIf (A−B)⊆C for this statement the Venn diagram is From the Venn diagram, it is clear thatIf A−B⊆C, and A⊆CNow ,if (A−C)⊆B for this statement the Venn diagram. from the Venn diagram, it is clear thatA∩B≠ϕ,A∩B⊆C and A−C=ϕ⊆B but A⊈B