Determine the truth value of the given compound proposition using 𝑥=𝑤=1;𝑧=0 ¬(𝑥⟶¬𝑧)⟷(𝑤∨𝑥)Group of answer choicesTrueFalse
Question
Determine the truth value of the given compound proposition using
x = w = 1; z = 0
¬(x ⟶ ¬z) ⟷ (w ∨ x)
Group of answer choices
- True
- False
Solution
To determine the truth value of the given compound proposition, we need to substitute the given values of x, w, and z into the proposition and then evaluate it step by step.
The given compound proposition is ¬(x⟶¬z)⟷(w∨x)
Step 1: Substitute the given values ¬(1⟶¬0)⟷(1∨1)
Step 2: Evaluate the negation and implication ¬(1⟶1)⟷(1∨1)
Step 3: Evaluate the implication and disjunction ¬(0)⟷(1)
Step 4: Evaluate the negation 1⟷1
Step 5: Evaluate the biconditional True
So, the truth value of the given compound proposition is True.
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