Q in description

Question

Write the converse of the following true conditional statement. If the converse is false, write a counterexample.

If , then .

1. If , then ; true.
2. If , then ; false. Counterexample: x = 27 and .
3. If , then ; false. Counterexample: x = 25 and .
4. If , then ; true.

Answer 1

if x<30 then x<20 is false

its converse, if x<20 then x<30

if x>20, then x> 30 is true

its converse, if x>30 then x>20 is false

the conditional and its converse are both true

only if its a biconditional, with the arrow pointing both ways

p if and only if q

p iff q

or

q iff p

also if both are false, then

its also a biconditional

p iff q

same relationship between inverses and contrapositives

or

q iff p

if you don't see it, construct a truth table

and calculate the truth values to see the equivalences

Answer 2

1. If , then ; false. Counterexample: x = 27 and .