Logical Reasoning

By the end of this lessons, students should be able to:

1. Construct statement in the form of implication “If p then q” by using their own words correctly.

2. Construct statement in the form of implication “p if and only if q” by using their own words correctly.

3. Construct the truth value of converse, inverse and contrapositive of an implication based on the questions given correctly. 

4. Compare the truth value of converse, inverse and contrapositive of an implication based on the questions given correctly. 

Implication

If you pay attention for today's lessons,

then you will definitely understand this topic.

Implication

p: If you pay attention for today's lessons,

q: then you will definitely understand this topic.

How can we represent an Implication?

Implication "If p, then q"

• p is denoted as the antecedent.

• q is denoted as the consequent.

Example

Implication 'If p, then q'

Multiple Choice

Form implication 'if p, then q' with:

Antecedent: p and q are even numbers.

Consequent: Sum of p and q is even number.

• If p and q are even numbers, then sum of p and q is even number.

• If sum of p and q is even number, then p and q are even numbers.

Identify the antecedent and consequent of the following implication.

"If a triangle ABC is an equilateral triangle, then each interior angle is 60 degree."

Answer:

Antecedent:

Consequent:

Implication

'p if and only if q'

An implication "p if and only if q" consists of:

• if p, then q

• if q, then p

Example:

If k is a prime number, then k has only two factors.

If k has only two factors, then k is a prime number

Answer:

Multiple Choice

Which is the correct statement for the following implication.
"If

 $-a^3=-8$  , then  $a$  is a positive integer."

•  $-a^3=8$  if and only if  $a$  is a positive integer.

•  $-a^3=-8$  if and only if  $a$  is positive integer.

•  $-a^3\ne-8$  if and only if  $a$  is positive integer.

•  $-a^3=-8$  if and only if  $a$  is a negative integer.

Construct and compare the truth value of converse, inverse and contrapositive.

State the differences between the four statements:

Write the converse, inverse and the contrapositive for the following implication.

1. If 2 is a positive number, then 2 is greater then 0.

2. If 5+2>6, then 2>6