Use Indirect Truth Tables to Determine Whether Each of the Following

question 56

Multiple Choice

use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
-(W $\lor$ X) ⊃ ∼(Y • ∼Z)
∼(Y • W) ⊃ ∼Z
∼(W $\lor$ X) $\lor$ Z / (Z $\lor$ W) ⊃ (X • Y)

• A) Valid
• B) Invalid. Counterexample when W is true and X, Y and Z are false
• C) Invalid. Counterexample when W and Y are true and X and Z are false
• D) Invalid. Counterexample when Y and Z are true and W and X are false
• E) Invalid. Counterexample when W, Y, and Z are true and X is false

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Definitions:

Function

A connection framework between a pack of inputs and a slew of endorsed outputs, ensuring each input leads to a distinct output.

Composition

In mathematics, the operation of applying one function to the results of another, denoted as \((f \circ g)(x) = f(g(x))\).

Function

A relationship or expression involving one or more variables.

Logarithm

A mathematical operation that determines the power to which a base must be raised to produce a given number.