Kenneth h rosen chapter 1 excercise 1.3 question 16

Question

Each of Exercises 16–28 asks you to show that two compound
propositions are logically equivalent. To do this, either show
that both sides are true, or that both sides are false, for exactly
the same combinations of truth values of the propositional
variables in these expressions (whichever is easier).

 

q16)Show that p ↔ q and (p ∧ q) ∨ (¬p ∧ ¬q) are logically
equivalent.

so my question is according to above statement how i prove logical equivalence cause i proved using TT and LOgical identities but what is exactly means of this statement

“ To do this, either show that both sides are true, or that both sides are false, for exactly
the same combinations of truth values of the propositional
variables in these expressions” i didnt understand what statement says

please tell

Answer 1

We can say A is logical equivalent to B means 

1. A→B and B→A both must be tautology, which refers A↔B must be tautology. As per (↔) truth table, it will be tautology only when A and B both are true or false.
2. Both A and B will have the same truth table.