This document discusses implications and their logical properties. It defines an implication as having an antecedent "p" and a consequent "q". Examples are given of identifying the antecedent and consequent of implications. The properties of converse implications are discussed, where the converse switches the antecedent and consequent. Examples are given of writing the converse of an implication and determining whether it is true or false. Finally, examples are provided of writing implications given an antecedent and consequent.

1. 4.4 implication
If p, then q
p = antecedent
q = consequent

2. Identify the antecedent and
consequent of each of the
following implication

3. Example 1
Implication : If ab = o, then a = 0 or b = o.
Antecedent :
Consequent :

4. Example 2
Implication : if θ is an obtuse angle, then 90⁰ < θ
< 180⁰.
Antecedent :
Consequent :

5. Example 3
If x + y > 0, then y > - x.
Antecedent :
Consequent :

6. Example 4
Implication : if it rains today, then I will stay at
home
Antecedent :
Consequent :

7. Example 5
Implication : if p = 5, then 3 p = 15.
Antecedent :
Consequent :

8. Example 6
Implication : if the polygon is a pentagon, then
the sum of its interior angles is equal to 540⁰.
Antecedent :
Consequent :

9. Example 7
Implication : if Mairin passes her piano
examination, then her mother will buy her a
new piano.
Antecedent :
Consequent :

10. p if and only if q
Implication 1 : if p, then q.
Implication 2 : if q , then p.

11. Write down two implications
based on each of the
following statements.

12. Example 1
P = - 3 if and only if p⁵ = -243
Implication 1 :
Implication 2 :

13. Example 2
8 > 6 if and only if 8 – 2 > 6 – 2.
Implication 1 :
Implication 2

14. Example 3
M∩N = Φ if and only if set M does not intersect
with set N.
Implication 1 :
Implication 2

15. Example 4
Two lines are parallel if and only if they do not
intersect with each other.
Implication 1 :
Implication 2

16. Example 5
(x – 3) ( x – 4) = 0 if and only if x = 3 or x = 4.
Implication 1 :
Implication 2

17. Example 6
Set A is a subset of B if and only if all the
elements of A are elements of B.
Implication 1 :
Implication 2

18. Example 7
Tan 45⁰ = 1 if and only if 3 tan 45⁰ + 2 = 5.
Implication 1 :
Implication 2

19. Example 8
X = 2 if and only if x – 2 = 0.
Implication 1 :
Implication 2

20. Based on the given antecedent and consequent,
construct a mathematical statement in the
form of
(a) if p, then q
(b) p if and only if q
antecedent : x is an even number
consequent : x is divisible by 2

21. Based on the given antecedent and consequent,
construct a mathematical statement in the
form of
(a) if p, then q
(b) p if and only if q
antecedent : A = Φ
consequent : n(A) = 0

22. Based on the given antecedent and consequent,
construct a mathematical statement in the
form of
(a) if p, then q
(b) p if and only if q
antecedent : m² = 16
consequent : m = ± 4

23. Converse of implication
•If p, the q
•Converse : If q, then p

24. State the converse for each of the implication
given and determine whether the converse is
true or false.
Implication : if x = 3, then x² = 9
Converse :
True/ false :

25. Example 2
Implication : if x > 8, then x > 5.
Converse :
True/ false :

26. Example 3
Implication : if q is a multiple of 10, then q is a
multiple of 5 .
Converse :
True/ false :

27. Example 4
Implication : if y < 6, then y < 4.
Converse :
True/ false :

28. Example 5
Implication : if x + 9 = 0, the x = ̶ 9.
Converse :
True/ false :

29. Example 6
implication : if P (1,1) and Q (4, 5), then the
length of PQ = 5.
Converse :
True/ false :

30. Example 7
Implication : if today is raining, then I will not go
to school.
Converse :
True/ false :