91Ó°ÊÓ

Formulate the symbolic expression in words using. \(p:\) You play football. q: You miss the midterm exam. \(r:\) You pass the course. $$ \neg q \wedge r $$

Formulate the symbolic expression in words using. \(p:\) You play football. q: You miss the midterm exam. \(r:\) You pass the course. $$ (p \wedge q) \vee(\neg q \wedge r) $$

Let \(P(x, y)\) be the propositional function \(x \geq y .\) The domain of discourse is \(\mathbf{Z}^{+} \times \mathbf{Z}^{+} .\) Tell whether each proposition is true or false. $$ \forall x \exists y P(x, y) $$

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

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

Represent the proposition symbolically by letting \(p:\) There is a hurricane. \(q:\) It is raining. Either there is a hurricane or it is raining (or both).

Draw a Venn diagram and shade the given set. $$ (B-\bar{C}) \cup((B-\bar{A}) \cap(C \cup B)) $$

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

Refer to a group of 191 students, of which 10 are taking French, business, and music; 36 are taking French and business; 20 are taking French and music; 18 are taking business and music; 65 are taking French; 76 are taking business; and 63 are taking music. How many are taking French and music but not business?

What is the literal meaning of each statement. What is the intended meaning? Clarify each statement by rephrasing it and writing it symbolically. All 74 hospitals did not report every month.