Topic: Discrete Mathematics from Textbook: Discrete Mathematics Introduction to Mathematical reasoning

Instructions: The argument could be valid, or exhibit the converse or the inverse error. Use symbols (p,q,r) to write the logical form of each argument. If the argument is valid, identify the rule of inference (converse or inverse) that guarantees its validity. Otherwise, state whether the converse or the inverse error is made.

Further Information: regular implication: p-->q = If p, then q . . . for the respective values of p and q

converse rule: q-->p

inverse rule: ~p-->~q

32) The argument is as follows:

If I get a Christmas bonus, I'll buy a stereo.

If I sell my motorcycle, I'll buy a stereo.

If I get a Christmas bonus or I sell my motorcycle, then I'll buy a stereo.

For the variables:

p=I get a Christmas bonus, q=I sell my motorcycle, r=I'll buy a stereo

One possible statement for "If I get a Christmas bonus, I'll buy a stereo"

p --> r

Find the equivalent form of the statements that using the equivalence:

p --> q is equivalent to ~p V q. Then determine if the converse or inverse rule was correctly used.