(d) VX € P(N), XCR. (e) In ɛ N, VX e P(N), |X| < n. (f) Vn e Z, 3X c N, |X| = n. (g) 3me Z, Vn € Z, m = n+5.

A conditional is a statement that contains a conjecture. O True O False

Complete the following truth table. Use T for True and F for False. You may add more columns.

Let p = False – Mike spoke at the engineer’s conference       q = True  -  Mike received the outstanding engineer’s award Find the truth value of the compound statement – If Mike did not receive the outstanding engineers award, then Mike did not speak at the engineer’s conference.

Suppose that the given statements are true. Find the other true statements. (a) Given: If the window is above the door, then Austin's cousin is a girl. Which statement must also be true? - If Austin's cousin is a girl, then the window is above the door. - If Austin's cousin is not a girl, then the window is not above the door. - If the window is not above the door, then Austin's cousin is not a girl. (b) Given: If the bike is fast, then Rachel sleeps on the floor. The bike is fast. Which statement must also be true? - The bike is not fast. - Rachel sleeps on the floor. - Rachel does not sleep on the floor. (c) Given: If David knows how to dance, then the tires are old. If the tires are old, then my favorite movie is being shown. Which statement must also be true? - If my favorite movie is being shown, then the tires are old. - If David knows how to dance, then my favorite movie is being shown. - If my favorite movie is being shown, then David knows how to…

What is the coefficient of x4y2z6 in the expansion of (3x2 + 2y + 3z3)6 ?

Alice and Belle are perfect logicians. Each of them is given a different fraction, of the form , where n is a positive integer. They only know their own number and they know it's a different fraction from the other. They need to tell whose number is larger. The following conversation occurs: Alice: "I don't know". Belle: "I don't know either." Alice: "I still don't know." Belle: “Now I know whose number is larger." Alice: "Now I know your number too." Who has the larger number? What is the difference of the denominators? (A) Alice. 1. (B) Alice. 2. (C) Belle. 1. (D) Belle. 2.