Suppose a and b are elements in a group such that | a| = 4, | b | = 2, and a^3b

Question

Suppose a and b are elements in a group such that | a| = 4, | b | = 2, and a^3b = ba. Find | ab |. A. 1 B. 2 c. 3 D. 4 E. 5. The logical equivalent statement for ~ (p ~ q) A. p Q B. ~ p ~ q C. ~ p q. D. ~ p q E. ~ p => q. At a conference, 12 members shook hands with each other before and after the meeting. How many total number of handshakes occurred? A. 100 B. 132 C. 145 D. 144 E. 121 If p q is TRUE, which one is FALSE? A. p q. B. ~ p ~ q. C. ~q ~p D. p q. E. ~ p q. The contrapositive of p q is? A. p q. B. ~p ~q C. ~q ~p D. p q E. ~p q. Given that P(A B) = 1/2, P(A) = 1/5, P(A B) = 1/8, find P(B). A. 17/40 B. 33/40 C. 23/40 D. 3/16 E. 5/16.

Explanation / Answer

(As per Chegg policy, only four questions will be answered. You need to post a separate question for the remaining answers)

18. ~ (p V ~q)

Applying DeMorgan's law

=> ~p ^ ~~q

=> ~p ^ q which is D.

19. The first member had a handshake with 11 others, the second with ten others (the first one is already counted) and so on. Thus the number of handshakes before the meeting

= 11 + 10 + 9 +......1 = 11*12/2 = 66

The number of handshakes after the meeting is the same i.e 66

So the total number = 66*2 = 132 which is B.

20. p ^ q is true only when p and q are both true. So both p and q are true.

A. p <=> q is true for p and q both being true.

B. ~p => ~q is true for both p and q being true.

C. ~q => ~p is again true for p and q both being true

D. p V q is true for both being true.

E. ~p ^ q is false as ~p is false and q is true. So this is the answer.

21. The contrapositive of p => q is ~q => ~p which is C.

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