Write a conditional statement. Write the converse, inverse and contrapositive for your statement and determine the truth value of each. if a statement's truth value is false, give a conunterexample.

If [tex] \text{ \underline{ hypothesis } } p [/tex], then [tex] \text{ \underline { conclusion } } q [/tex] or mathematically [tex] p\rightarrow q [/tex].

Converse statement of [tex] p\rightarrow q [/tex] is statement [tex] q\rightarrow p [/tex].

If you negate (that means stick a "not" in front of) both the hypothesis and conclusion, you get the inverse:

[tex] \neg p\rightarrow \neg q [/tex].

Finally, if you negate everything and flip p and q (taking the inverse of the converse) then you get the contrapositive:

[tex] \neg q\rightarrow \neg p [/tex].

Example:

1. Statement: If it is raining, then I'm at home. (true)

2. Converse: If I'm at home, then it is raining. (not necessarily true)

3. Inverse: If it is not raining, then I'm not at home. (not necessarily true)

4. Contrapositive: If I'm not at home, then it is not raining. (true)

obasola1 obasola1 · Answer 2 · 2020-02-10T11:03:30+01:00

Answer:

if the weather is nice, then i will go out

converse q---->p if i go out, then the weather is nice

inverse ~p---.~q if the weather is not nice, then i will not go out

contrapositive ~q--->~p if i don't go out, then the weather is not nice

Step-by-step explanation:

consider the statement below

if the weather is nice, then i will go out

we designate the first part of the statement as p, and the other part as q

p=if the weather is nice

q=then i will go out

we can get the negations for this statement as

~p=if the weather is not nice

~q=then i will not go out

converse q---->p if i go out, then the weather is nice

inverse ~p---.~q if the weather is not nice, then i will not go out

contrapositive ~q--->~p if i don't go out, then the weather is not nice