Page 40 - ADVANCED MATH F.5

Form Five Form Five

12. (a) Not a tautology (b) Not a tautology

13. (a) (i)( pq∧ ) r∨≡ Lightness is clever and polite or she is humble.

(ii)  pq∨ ≡ Lightness is not clever or she is humble.
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(b) (i) ( pq∨ ) ∧ p →  q (ii) (qr∨ )∧  p
(iii) ( q∧  ) r →   p

14. (a) Valid (b) Valid (c) Not valid (d) Valid
(e) Valid (f) Not valid (g) Valid (h) Not valid

(i) Not valid (j) Not valid

16. (a) p ∧ (qr∨ ) s∧ (b) ( p∨ ) r ∨  [( pq∨ )(qr∧ ∨ ] )

(c) pqr∨∨

17. (a) ( p∧ q ∨  ) ( pq∧ )

(b) ( pqr∧∧ ) ( ∨ pqr∧∧ ) ( ∨ p∧  q∧  ) r

18. (a) Tautology (b) Not a tautology

19. = ∨
pq∧
*
~ q r
20. (a) T T
1 2
q
(b) ~ q: T T
1 2

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Mathematics for Advanced Secondary Schools

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ADVANCED MATH F.5 TG CHAPTERS.indd 34