E12

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 this month is June, next month is July

converse-->if next month is July, this month is June

This is a true statement !!!

 

if and only if statement:

-->statements with a true converse can be worded into an if and only if statement

example-->next month is July if and only if, this month is June

 

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:

state the converse of this statement:yesterday was saturday so, today is sunday

is it a true statement?

if so write it as a if and only if statement. 

 

answer:

converse-->today is sunday so, yesterday was saturday

yes it is true

if and only if statement-->yesterday was saturday if and only if, today is sunday

 

 

nicoleasprey//tomblackburn