Maharashtra State Board course HSC Science (General) 12th Board Exam
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Without using truth table show that P↔q ≡(P ∧ q) ∨ (~ p ∧ ~ q) - Mathematics and Statistics

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Question

Without using truth table show that P↔q ≡(P ∧ q) ∨ (~ p ∧ ~ q)

Solution

`L.H.S= pq-=(p ->q) ^^ (q->p)`

`-=(~p vv q) ^^ (~q vv p)`

`-=[~p^^(~qvvp)]vv[q^^(~qvvp)]  " by distributive law"  `

 `-=[(~p^^~q)vv(~p^^p)]vv[(q^^~q)vv(q^^p)]    " by distributive law"`

`-=[(~p^^q)vvF]vv[Fvv(q^^p)] "by complement law"  `

`-=(~p^^~q)vv(q^^p)  " by identity law"`

`-=(p^^q)vv(~p^^~q) " by commutative law"`

=R.H.S

  Is there an error in this question or solution?

APPEARS IN

 2012-2013 (March) (with solutions)
Question 2.1.1 | 3.00 marks
Solution Without using truth table show that P↔q ≡(P ∧ q) ∨ (~ p ∧ ~ q) Concept: Mathematical Logic - Algebra of Statements.
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