Suppose a, b € Z. If both ab and a+b are even, then both a and b are even. Suppose n € Z. If 3 n², then 3 n.

5. B= { ,.-} is compact.

a. Without tables, show that -(p v (-p ^g)) a nd -p ^-q are logically equivalent.

assume that A={6,8,4,g} and B={3,2,8,d,h,g}. (a) n(A×B)= (b) n(B×B×B)=

a) Show that by using Laws that if the compound statement is logically equal. [p ^ (~ (~pVq))] V (p^q) = p

verify that (A + B)C = AC + BC

Let P(x) be the statement "x^2−x−20⩽0". a. If the domain consists of −4,0,1 and 2, then "∀x,P(x)" is: True or False? b. If the domain consists of -5,-4,0, and 6, then "∀x,P(x)" is: True or False? Now let Q(x) be the statment "x^2 - x - 20 > 0." a. If the domain consists of -5,2,4, and 6, then "∃x such that Q(x)" is:True or False? b. If the domain consists of -1,0,1, and 4, then "∃x such that Q(x)" is: True or False?

prove if a and b are both odd integer, then 16/ (a^4) + (b^4) -2. Aimages O videgs

A. TRUE OR FALSE. Determine each of the following statements if it is true or false. Support your answer by proving or giving examples 1. If p is prime such that p divides a^2 then p divides a 2. If a^3 divides c^2, then a divides c 3. If p is prime, p divides a^2 +b^2 and p divides b^2 + c^2, then p divides a^2 + c^ A Gc

Which of the following is a contradiction? ○ ((PVQ) ⇒~ R) ^ (P^ QAR) O ((PVQ) ⇒~ R) ^ (Q⇒ (RV P)) O ((P VQ) ⇒~ R) V (Q⇒ (RV P)) O ((PVQ) ~ R) ^ (P^Q^~ R)