Logic Symbols and Biconditionals

If a represents "Brent works this summer" and b represents "Brent takes a vacation" which symbols best represent the statement "If Brent works this summer then he will not take a vacation."

• a → b

• a ∨ b

• a → ~ b

• a ∧ ~ b

If a represents "Brent works this summer" and b represents "Brent takes a vacation" which symbols best represent the statement "Brent will work and take a vacation this summer."

• a → b

• a ∧ b

• a ∨ b

• a ↔ b

If a represents "Brent works this summer" and b represents "Brent takes a vacation" which symbols best represent the statement "Therefore, Brent will not take a vacation."

• ∴ ~b

• ∴ ~a

• → ~b

• → ~a

If a represents "Two angles are vertical angles" and b represents "The angles are congruent" which symbols best represent the statement "If two angles are not congruent, then the angles are not vertical angles."

• a → b

• ~a → ~b

• b → a

• ~b → ~a

Tags

CCSS.HSG.CO.C.9

If a represents "Two angles are vertical angles" and b represents "The angles are congruent" which symbols best represent the statement "Two angles are not vertical angles and the angles are congruent"

• a ∧ b

• a ∨ b

• ~a ∨ b

• ~a ∧ b

If a represents "Two angles are vertical angles" and b represents "The angles are congruent" which symbols best represent the statement "Two angles are vertical angles if and only if they angles are congruent." (and yes, this is a false statement)

• a ↔ b

• a → b

• a ∴ b

• a ∨ b

Which is a counterexample for the following conditional:
If an electronic device has a screen then it is a television.

• television
• cell phone
• computer mouse
• keyboard

What is the biconditional statement of the following conditional statement?
“If Shelly lives in Texas, then she lives in the United States.”

• If Shelly lives in Texas, then she lives in the United States.
• If Shelly lives in the United States, then she lives in Texas.
• Shelly lives in Texas if and only if she lives in the United States.
• If Shelly does not live in Texas, then she does not live in the United States.

Which of the following is a biconditional statement?

• If you do not vote, then you are not at least 18 years old.

• You can vote if and only if you are 18 years old.

• If you are 18 years old, then you can vote.

• Then you can vote if you are 18 years old.

Given, "If I have a Siberian Husky, then I have a dog." Identify the converse.

• If I do not have a Siberian Husky, then I do not have a dog.
• If I have a dog, then I have a Siberian Husky.
• If I do not have a dog, then I do not have a Siberian Husky.
• If I do not have a Siberian Husky, then I have a dog.