Introduction to Logic Proofs

Which is a valid conclusion for....

If I run in the morning then I feel energized

If I am energized then I have a great day

• If I am energized then I have a great day

• I have a great day

• I am energized

• If I run in the morning then I have a great day

Let p represent "x is an even number" and q represent "x is divisible by 4" Which of the following is true when x = 10?

• 

  $p\wedge q$

• $p\vee q$

• $\sim p$

• $q$

What is the converse of the statement "If it is Sunday, then I don't go to school"?

• If it is not Sunday, then I do not go to school.

• If I go to school, then it is not Sunday

• If I do not go to school, then it is Sunday.

• If it is not Sunday, then I go to school

When the statement" If A then B" is true, which one of the following must also be true?

• If B, then A

• If not B, then A

• If not A, then B

• If not B, then not A

What is the contrapositive of the statement "If I study, then I pass the test"?

• I pass if I study

• If I pass the test, then I study

• If I do not study, then I do not pass

• If I do not pass the test, then I did not study

What is the contrapositive of the statement

 $q\rightarrow\sim p$  

•  $\sim q\rightarrow p$  

•  $p\rightarrow\sim q$  

•  $\sim p\rightarrow q$  

•  $\sim p\rightarrow q$  

Assign truth values to the variables to make the premises true. Use the Laws of Inference to choose a valid conclusion for:

• r

• p

• q

• ~r

Which is a valid conclusion?

• a

• b

• c

• ~c

Which is a valid conclusion?

• j

• ~j

• k

• ~k

• i

Which is a valid conclusion?

• d

• y

• n

• h