Answer to Question #311723 in Discrete Mathematics for Showi

Question

Determine whether ( 𝑝∨𝑞)∧(𝑝→𝑟)∧( 𝑞→𝑠)→𝑟∨𝑠 is a Tautology or a contradiction using a truth table

Give full truth table

Answer 1

Solution

The truth table for $(p∨q) ∧(p→r) ∧(q→s) → r∨s$ is shown below

From the last column, we can see that, all TRUE

Therefore,

$(p∨q) ∧(p→r) ∧(q→s) → r∨s$ is a Tautology