Page 246 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

npvnq:
(b)
Sheron Simpson is not a Jamaican track and field athlete or Don Quarrie is not a former Jamaican track and field athlete.
The two English sentences mean the same thing.
5. (a) p → nq
6. (a) np ^ q
(b) nq → p (b) np v nq
In questions 7 to 10 construct a truth table for
each of the compound propositions.
7. (a) p → nq
8. (a) np ^ q
9. (a) nq → np
10. (a) np v q
11. Show that p
equivalent
12. Show that p
13. Show that p
equivalent.
14. Show that p
(b) p → np (b) q → p (b) np → nq
(b) np ^ nq
→ q and nq → np are logically
→ q 􏰀 np v q.
v q and np → q are logically
p
q
p^q
n(p^q)
T
T
T
F
T
F
F
T
F
T
F
T
F
F
F
T
p
q
np
nq
npvNq
T
T
F
F
F
T
F
F
T
T
F
T
T
F
T
F
F
T
T
T
From the truth tables:
n(p ^ q) 􏰀 n p v n q.
Hence the compound propositions are logically equivalent.
EXERCISE 11.9
In questions 1 to 6:
Let p: Yuri Goorgorin was a Russian
And q: Coheddi Jagon was president of Guyana.
Express each of the following propositions as an English sentence.
^ q 􏰀 n(p → nq) 15. Show that n(p → q) 􏰀 p ^ nq
16. Show that n(p v q) and np ^ nq are logically equivalent.
1. (a) np
2. (a) p ^ q
3. (a) p → q
4. (a) np → nq
(b) nq (b) p v q
(b) q → p (b) nq → np
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17.