If you did not study hard you will not earn an A on the test

If you did not study hard you will not earn an A on the test

You studied hard

Therefore, you will earn an A on this test

A. Identify the statements and label them with p, q, r, etc

B. Write the agrument in symbolic form

C. Identify the premises in symbolic form

D. Identify the conclusion in symbolic form

E. Create a truth table for the arguement

F. Determine if the arguement is valid and explain why or why not

Solution

A)

You studied hard (p)

you will earn an A on this test (q)

B)

If you did not study hard you will not earn an A on the test (~p ---> ~q)

You studied hard (p)

Therefore, you will earn an A on this test (q)

symbolic form

((~p --> ~q)^p) --->q

C)

premise 1 : If you did not study hard you will not earn an A on the test (~p --> ~q)

premise 2 : You studied hard (p)

D)

conclusion : Therefore, you will earn an A on this test (q)

E) Truth Table

p       q        ~p      ~q    ~p-->~q     (~p-->~q)^p     (~p-->~q)^p-->q

T       T        F         F         T                T                        T

T       F        F         T          T                T                        F

F       T        T         F          F       F                         T

F       F        T         T          T                F                         T

F) The argument is not valid because the argument as a whole is not always true(see above the underlined false)