outcome:
E12:demonstrate an understanding of the concept of converse
converse statements
-->if one thing is true, then is the opposite?
-->if p, then q but,
-->not every statement has a true converse statement
true converse statement:
statement--> If water can be turned into ice, then ice can be turned into water
converse-->If ice can be turned into water, then water can be turned into ice
This is a true statement !!!
if and only if statement:
-->statements with a true converse can be worded in an if and only if statement
example-->
untrue converse statement:
statement-->if you've been swimming, your hair is wet
converse-->if your hair is wet, you've been swimming
*this converse statement is not true because it is not so in every case
converse statements in circle geometry:
statement-->if a line is perpendicular to a chord and passes through the centre of a circle then, it bisects the chord
converse-->if a line is perpendicular to a chord and bisects the chord than, it passes through the centre of the circle
if and only if statement-->a line is perpendicular to a chord of a circle and bisects the chord if and only if, it passes through the centre of the circle
sample problem: Does this statement have a true converse statement. If so write it as a if and only if statement.
Question: If next month is July, then this month is June
answer:Yes is does. If this month is June, then next month is July.
If next month is July IFF this month is June
Nicole and Tommy
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