Q12 of 162 Page 1

If A is any set, prove that: A ϕ A=ϕ.

We need to show A and B are equal for that we must show A B and B A.


We have s A ϕ (∵ ϕ is a subset of every set)


∴ ϕ A.


Hence A =ϕ.


Suppose A = ϕ


∵ Every set is subset of itself


∴ ϕ = A ϕ


Hence, Proved.


More from this chapter

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(i) {1,2}


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(iii) {1}

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What is the total number of proper subsets of a set consisting of n elements?

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Prove that: A B, B C and C A A = C.

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