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1. Suppose P and Q are the statements: P: Jack passed math. Q: Jill passed math.(25...

1. Suppose P and Q are the statements: P: Jack passed math. Q: Jill passed math.(25 points)

(a) Translate “Jack and Jill both passed math” into symbols.

(b) Translate “If Jack passed math, then Jill did not” into symbols.

(c) Translate “P ∨ Q” into English.

(d) Translate “¬(P ∧ Q) → Q” into English.

(e) Suppose you know that if Jack passed math, then so did Jill. What can you conclude if you know that: i. Jill passed math? ii. Jill did not pass math?

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