Three projects X, Y, Z: At least one receives funding. If X receives funding, Y does not. Z receives funding only if X does. If Y receives funding, what is true?
Answer and explanation
Correct answer: B. Neither Project X nor Project Z receives funding
- Step 1: Y is funded. From X -> ~Y, contrapositive is Y -> ~X. Thus ~X (X not funded). Step 2. From Z -> X, contrapositive is ~X -> ~Z. Thus ~Z (Z not funded). Step 3. Neither X nor Z is funded. Answer: Neither Project X nor Project Z receives funding. Why not the others: X and Z cannot be funded.
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