Question

Use Truth Table to determine whether (¬p → q) ^ (¬pVq) = q

2. Suppose that Q(x) is "x+1=2x", where x is a real number. Find the truth value of the following statement:
a) Q(1)
b) vQ(x)
c) Q(x)
3. What is the power set of the set {Ø, a, b}
4. Express the negations of each of these statements so that all negation symbols immediately precede predicates
a) xyz P(x,y,z)
b) Vxy P(x, y)VQ(x, y)

Answer 1

To determine the truth value of an expression, use a truth table. The truth values of specific statements can be found by substituting values. The truth value of an expression with a variable cannot be determined without a specific value.

Step-by-step explanation:

A)

To determine the truth value of (¬p → q) ^ (¬pVq) = q2, we can use a truth table. Let's assign p and q the truth values T and F respectively. (¬p → q) ^ (¬pVq) can be simplified as (F → F) ^ (T V F), which is equivalent to T ^ T. Since both T and T evaluate to T, the statement (¬p → q) ^ (¬pVq) = q2 is true.

B)

To find the truth value of Q(1), we substitute 1 for x in the equation Q(x) = x + 1 = 2x. Q(1) becomes 1 + 1 = 2 * 1, which simplifies to 2 = 2. Therefore, the truth value of Q(1) is true.

C)

The truth value of vQ(x) is dependent on the value of x. Since we don't have a specific value for x, we cannot determine the truth value of vQ(x).