91Ó°ÊÓ

Let \(a, b,\) and \(c\) be any real numbers. Then \(a

Let UD = set of integers, \(P(x, y): x\) is a multiple of \(y,\) and \(Q(x, y): x \geq y\) Determine the truth value of each proposition. $$(\exists x) \mathrm{P}(15, x)$$

Mark each sentence as true or false, where \(p, q,\) and \(r\) are arbitrary statements, \(t\) a tautology, and \(f\) a contradiction. $$\text { If } p \vee q \equiv p \vee r, \text { then } q \equiv r$$.

Let \(a, b,\) and \(c\) be any real numbers. Then \(a

Use De Morgan's laws to verify each. (Hint: \(p \rightarrow q \equiv \sim p \vee q\) ). $$\sim(\sim p \wedge \sim q) \equiv p \vee q$$

Determine whether or not the assignment statement \(x \leftarrow x+1\) will be executed in each sequence of statements, where \(i \leftarrow 2, j \leftarrow 3, k \leftarrow 6,\) and \(x \leftarrow 0\). $$ \begin{array}{l} \text { If }(i<3) \wedge(j<4) \text { then } \\ \qquad x \leftarrow x+1 \end{array} $$ else $$ y

Let \(a, b,\) and \(c\) be any real numbers. Then \(a

Use De Morgan's laws to verify each. (Hint: \(p \rightarrow q \equiv \sim p \vee q\) ). $$\sim(\sim p \vee q) \equiv p \wedge \sim q$$

Determine whether or not the assignment statement \(x \leftarrow x+1\) will be executed in each sequence of statements, where \(i \leftarrow 2, j \leftarrow 3, k \leftarrow 6,\) and \(x \leftarrow 0\). $$ \begin{array}{l} \text { If }(i4) \text { then } \\ x \leftarrow x-1 \end{array} $$ else $$ x

Let \(a, b,\) and \(c\) be any real numbers. Then \(a