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Math  /  Discrete

Questionthe simple statements p: There is a fire in the fireplace. qq : The house is cold. ch each compound statement to its symbolic form. There is a fire in the fireplace if and only if the house is not cold. If there is a fire in the fireplace then the house is not cold. There is no fire in the fireplace and the house is cold. a. ∼p∨q\sim p \vee q There is a fire in the fireplace or the house is not cold. b. ∼p∧q\sim p \wedge q There is no fire in the fireplace or the house is cold. c. ∼p↔q\sim p \leftrightarrow q
d. q→∼pq \rightarrow \sim p e. p∧∼qp \wedge \sim q
There is no fire in the fireplace if and only if the house is cold. f. p↔∼qp \leftrightarrow \sim q
There is a fire in the fireplace and the house is not cold. g. p→∼qp \rightarrow \sim q If the house is cold then there is no fire in the fireplace. h. p∨∼qp \vee \sim q

Studdy Solution
Translate: "If the house is cold then there is no fire in the fireplace." Symbolic form: q→∼p q \rightarrow \sim p
The symbolic forms of the compound statements are as follows: a. ∼p∨q \sim p \vee q b. ∼p∧q \sim p \wedge q c. ∼p↔q \sim p \leftrightarrow q d. q→∼p q \rightarrow \sim p e. p∧∼q p \wedge \sim q f. p↔∼q p \leftrightarrow \sim q g. p→∼q p \rightarrow \sim q h. p∨∼q p \vee \sim q

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