Question is from The Logic Book 6th Edition 53E 3 Prove that

Question is from The Logic Book 6th Edition 5.3E

3. Prove that each of the folloiwng is a theorem in SD (= is used to symbolize biconditional) using derivations

j) (A & A) = A

Solution

I am solving it using the truth table

Hence the value of A&A is equal to A

Logical Proof:

Let the element a belongs to A & A, then element must belong to

(a belongs to A) and (a belongs to A)

Hence we get a belongs to A

Therefore, A is a subset of A & A

Let the element of a belongs to A

then (a belongs to A) and (a belongs to A)

Hence we get a belongs to A & A

Therefore, A&A is a subset of A

Hence we get A&A = A