I have a textbook that I got through Chegg (Discrete Mathematics, B.Ross & C.Wri
ID: 2943552 • Letter: I
Question
I have a textbook that I got through Chegg (Discrete Mathematics, B.Ross & C.Wright, 5th ed) but I don't seem to find it in Cramster. There's a couple of questions that are not answered in the book. I was hoping someone could help me find the answers.
*some browsers won't display special characters. so I'm gonna try the HTML code. I couldn't find the HTML code for logical equivalence. I used <=>
Prove or Disprove:
1. [p ( q r )] <=> [( p q ) ( p r )]
2. [p (q r)] <=> [(p q) (p r)]
3. [( p q) r] <=> [p (q r)] this is logically equivalent but how would I prove it? Can I just say by associative law?
4. [( p q) r] <=> [p (q r)] this is logically equivalent but how would I prove it?Can I just say by associative law?
5. (p q) r <=> (p q) r this is logically equivalent but how would I prove it? Can I just say by associative law?
Thanks for the help!
Explanation / Answer
I have a textbook that I got through Chegg (Discrete Mathematics, B.Ross & C.Wright, 5th ed) but I don't seem to find it in Cramster. There's a couple of questions that are not answered in the book. I was hoping someone could help me find the answers.
*some browsers won't display special characters. so I'm gonna try the HTML code. I couldn't find the HTML code for logical equivalence. I used <=>
Prove or Disprove:
1. [p ( q r )] <=> [( p q ) ( p r )]
2. [p (q r)] <=> [(p q) (p r)]
3. [( p q) r] <=> [p (q r)] this is logically equivalent but how would I prove it? Can I just say by associative law?
4. [( p q) r] <=> [p (q r)] this is logically equivalent but how would I prove it?Can I just say by associative law?
5. (p q) r <=> (p q) r this is logically equivalent but how would I prove it? Can I just say by associative law?
FOR ALL THESE QUESTIONS YOU CAN USE TRUTH TABLE OR LOGIC ..
JUST SHOWING YOU AN EXAMPLE ..COMPLETE TRUTH TABLE FOR 3 VARIABLES P,Q,R WOULD HAVE
THE FOLLOWING ENTRIES ..USING 0 FOR FALSE AND 1 FOR TRUTH.
P
Q
R
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
STANDARD TRUTH TABLES FOR IMPLICATION STATEMENT AND UNION ARE
IMPLICATION…
P
Q
P IMPLIES Q
1
1
1
1
0
0
0
1
1
0
0
1
EQUIVALECE ..TWO WAY IMPLICATION
P
Q
P EQUIVALENT TO Q
1
1
1
1
0
0
0
1
0
0
0
1
UNION
P
Q
P + Q
1
1
1
1
0
1
0
1
1
0
0
0
INTERSECTION
P
Q
P * Q
1
1
1
1
0
0
0
1
0
0
0
0
USING THE ABOVE YOU CAN PROVE ALL
TRY AND IF INDIFFICULTY PLEASE COME BACK
P
Q
R
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
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