91Ó°ÊÓ

Determine the truth value of each statement. The domain of discourse is \(\mathbf{R}\). Justify your answers. $$ \exists x\left(x^{2}>x\right) $$

Formulate the symbolic expression in words using \(p:\) Today is Monday, \(q:\) It is raining, \(r:\) It is hot. $$ \neg q \rightarrow(r \wedge p) $$

Represent the proposition symbolically by letting \(p:\) There is a hurricane. \(q:\) It is raining. Either there is a hurricane or it is raining, but there is no hurricane.

Draw a Venn diagram and shade the given set. $$ (A \cup B)-B $$

Determine the truth value of each statement. The domain of discourse is \(\mathbf{R}\). Justify your answers. $$ \forall x\left(x>1 \rightarrow x^{2}>x\right) $$

Formulate the symbolic expression in words using \(p:\) Today is Monday, \(q:\) It is raining, \(r:\) It is hot. $$ \neg p \rightarrow(q \vee r) $$

Formulate the symbolic expression in words using \(p:\) Today is Monday, \(q:\) It is raining, \(r:\) It is hot. $$ \neg(p \vee q) \leftrightarrow r $$

Represent the proposition symbolically by letting \(p:\) You run laps daily. \(q:\) You are healthy. \(r:\) You take multi-vitamins. You run 10 laps daily, but you are not healthy.

Determine the truth value of each statement. The domain of discourse is \(\mathbf{R}\). Justify your answers. $$ \exists x\left(x>1 \rightarrow x^{2}>x\right) $$

Represent the proposition symbolically by letting \(p:\) You run laps daily. \(q:\) You are healthy. \(r:\) You take multi-vitamins. You run 10 laps daily, you take multi-vitamins, and you are healthy.