Logic

Given that p = “I have three cats” and q = “I am insane”, write the following statement in symbolic notation:

I do not have three cats.

• ¬ p

• ¬ q

• ^ p

• ^ q

Given that p = “I have three cats” and q = “I am insane”, write the following statement in symbolic notation:

If I have three cats, then I am insane.

• q => p

• p => q

• p v q

• p ^ q

Given that p = “I have three cats” and q = “I am insane”, write the following statement in symbolic notation:

If I am not insane, then I do not have three cats.

• ¬ q => p

• ¬ p => q

• ¬ q => ¬ p

• ¬ p => ¬ q

Given that p = “I have three cats” and q = “I am insane”, write the following statement in symbolic notation:

I have three cats if and only if I am insane.

• q => p

• p => q

• q <=> p

• p <=> q

Given that p = “I have three cats” and q = “I am insane”, write the following statement in symbolic notation:

If I am insane, then I have three cats.

• q => p

• p => q

• q <=> p

• p <=> q

Given the statement, "If I have three cats, then I am insane”, write the converse of the statement.

• If I have three cats, then I am insane.

• If I am not insane, then I do not have three cats.

• If I am insane, then I have three cats.

• If I do not have three cats, then I am not insane.

Tags

CCSS.RI.7.8

CCSS.RI.8.1

CCSS.RL.11-12.1

CCSS.RL.7.1

CCSS.RL.9-10.1

Given the statement, "If I have three cats, then I am insane”, write the inverse of the statement.

• If I have three cats, then I am insane.

• If I am not insane, then I do not have three cats.

• If I am insane, then I have three cats.

• If I do not have three cats, then I am not insane.

Tags

CCSS.RI.7.1

CCSS.RI.7.8

CCSS.RL.7.1

CCSS.RL.8.1

CCSS.RL.9-10.1

Given the statement, "If I have three cats, then I am insane”, write the contrapositive of the statement.

• If I have three cats, then I am insane.

• If I am not insane, then I do not have three cats.

• If I am insane, then I have three cats.

• If I do not have three cats, then I am not insane.

Tags

CCSS.RI.7.1

CCSS.RI.7.8

CCSS.RI.8.1

CCSS.RL.11-12.1

CCSS.RL.9-10.1

Which statement is logically equivalent to p => q ?

• ¬ p => ¬ q

• ¬ q => ¬ p

• q => p

Tags

CCSS.7.SP.C.5

State whether the argument below is valid or invalid. If it is invalid, give a reason why it is invalid.

If Joe eats greasy food, he will feel sick.

Joe does not eat greasy food.

Therefore, Joe won’t feel sick.

• valid

• invalid, inverse error

• invalid, converse error

Tags

CCSS.RI.7.1

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.7.1

CCSS.RL.8.1