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

Concept: Increasing and Decreasing Functions

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