Maharashtra State BoardHSC Commerce 12th Board Exam
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Using truth table show that – (p → – q) ≡ p ∧ q - Mathematics and Statistics

Sum

Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q 

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Solution

∼ (P → ∼ q) ≅ P ∧ q 

=`(e^x/(2e^y))=1/2[e^(x-y)]` 

`dy/dx=1/2[e^x+e^y]` 

Truth table 

P (1) q(2) ∼q(3) p→∼q (4) ∼(p→∼q)(5) p^q(6)
T T F F T T
T F T T F F
F T F T F F
F F T T F F

From the truth table, we get 5th and 6th columns are
identical 

∴∼(p→∼q)≅ p∧q

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