Computer Science – 3.2 Logic Gates and Logic Circuits | e-Consult
3.2 Logic Gates and Logic Circuits (1 questions)
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The logic expression representing "The ground is wet if and only if it is raining or the weather is sunny" is C ↔ (B ∨ A) (C if and only if (B or A)). This expresses the biconditional relationship.
Given that A is true and B is false, we evaluate the expression:
- B ∨ A
- False ∨ True
- True
- C ↔ (B ∨ A)
- C ↔ True
- The biconditional is true only if both sides have the same truth value. Therefore, C must also be true.
Therefore, the statement is true only if C is true. Without knowing the value of C, we cannot definitively say whether the overall expression is true or false. However, for the expression to be true, C must be true.