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In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (i) If x ∈ A and A ∈ B , then x ∈ B

Q2. In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

(i) If x \in A and A \in B , then x \in B

Answers (1)
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The given statment is false,

example: Let A = { 2,4 }

                     B = { 1,{2,4},5}

                     x be 2.

          then, 2 \in   { 2,4 } = x \in A and { 2,4 } \in { 1,{2,4},5} = A \in B 

             But 2 \notin { 1,{2,4},5}  i.e. x \notin B

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