Page 31 - ADVANCED MATH F.5

Form Five Form Five

(c) Inverse: If industries are not in harmony with the surroundings,
then they are not environmentally friendly.
Converse: If the industries are environmentally friendly, then
they are in harmony with the surroundings.
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Contrapositive: If the industries are not environmentally
friendly, then they are not in harmony with the surroundings.

(d) Inverse: If ABC is not an equilateral triangle, then it is not a
right-angled triangle.
Converse: If ABC is a right-angled triangle, then it is an
equilateral triangle.
Contrapositive: If ABC is not a right-angled triangle, then it
is not an equilateral triangle.

(e) Inverse: If f (x) is not a rational function, then it has no
asymptotes.
Converse: If f (x) has asymptotes, then it is a rational function.
Contrapositive: If f (x) has no asymptotes, then it is not a
rational function.

2. (a) p q ~ p q → ~ p (q → ~)p → p

T T F F T
T F F T T
F T T T F
F F T T F

(b) p q ~ p q → ~ p ~(q → ~ )p ~(q → ~ )p → ~ p

T T F F T F
T F F T F T
F T T T F T
F F T T F T

25
Mathematics for Advanced Secondary Schools

30/06/2024 18:01:49
ADVANCED MATH F.5 TG CHAPTERS.indd 25
ADVANCED MATH F.5 TG CHAPTERS.indd 25 30/06/2024 18:01:49