QuestionLet be "The campus is closed" and be "It is Sunday." Express "Being Sunday is necessary and sufficient for the campus being closed" symbolically.
Studdy Solution
STEP 1
Assumptions1. The statement "p The campus is closed" is represented by the symbol p. . The statement "q It is Sunday" is represented by the symbol q.
STEP 2
The phrase "Being Sunday is necessary and sufficient for the campus being closed" can be broken down into two parts "Being Sunday is necessary for the campus being closed" and "Being Sunday is sufficient for the campus being closed".
STEP 3
The statement "Being Sunday is necessary for the campus being closed" means that if the campus is closed, then it is Sunday. This can be written in symbolic form as p implies q, or p -> q.
STEP 4
The statement "Being Sunday is sufficient for the campus being closed" means that if it is Sunday, then the campus is closed. This can be written in symbolic form as q implies p, or q -> p.
STEP 5
The phrase "Being Sunday is necessary and sufficient for the campus being closed" is a combination of the two statements from steps3 and4. This can be written in symbolic form as p if and only if q, or p <-> q.
So, the symbolic form of the compound statement "Being Sunday is necessary and sufficient for the campus being closed" is p <-> q.
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