Question

if p and q are two propositions,use truth table technique to show that a) (p=q) ^ (q=p)= p=q and b) [(p=q) ^ p]=q is a Tautology​

Answer 1

see attached

Explanation:

The truth table technique shows the first proposition is True. However, the second proposition cannot be shown to be a tautology, because it isn't true.

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a.

The "equals" relation is commutative: (a=b) ≡ (b=a), hence the expression ...

(p=q)∧(q=p)

is equivalent to

(p=q)∧(p=q)

We know that the And of p with itself is just p, so that fact ensures the truth of ...

(p=q)∧(p=q) = (p=q)

Hence

(p=q)∧(q=p) = (p=q)

The top truth table in the attached shows the final comparison of the two expressions is true for all values of p and q.

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b.

The attached truth table shows that the given relation is not a tautology.