Loading....
Coupon Accepted Successfully!

 

Implications


If two statements are connected by “if-then”, “only if” and “if and only if”, they are called implications.Such statements are very common in mathematics.

Example 1:
If a triangle is right angled, then the square on the hypotenuse is equal to the sum of the squares on the other two sides.

Solution:
: A triangle is right angled
: The square on the hypotenuse is equal to the sum of the squares on the other two sides.
We have combined these statements by “if-then” implication. The resulting statement is ; which means if , then .

Example 2:
A quadrilateral is a parallelogram only if the diagonals bisect each other.

Solution:
p: a quadrilateral is a parallelogram
q: diagonals bisect each other.
We have combined the two statements with “only if” implication.
i.e. the 1st part is dependant on the 2nd part or it is equivalent to q p.

Example 3:
Two triangles are congruent if and only if their corresponding sides are equal.

Solution:
p: Two triangles are congruent
q: Their corresponding sides are equal
This is a two way implication
i.e.  p q is if then
and p q is only if
p q is if and only if.




Test Your Skills Now!
Take a Quiz now
Reviewer Name