Symbolic Logic

Given Let c represent "∠A and ∠B are congruent."

Let d represent "∠A and ∠B have the same measure."

Translate the following argument into symbolic form:

∠A and ∠B are congruent if and only if they have the same measure.

∠A and ∠B have different measures.

Therefore, ∠A and ∠B are not congruent.

Let p represent "Two angles are complementary."

Let q represent "Two angles form a straight angle."

What is the symbolic representation of the following statement?

If two angles form a straight angle, then they are not complementary.

• p→¬q

• q→p

• p→~q

• q→~p

Let

• p: A zebra has a mane.

• q: A dog can bark.

Match each statement to its symbolic form:

• A zebra does not have a mane.

• If a zebra does not have a mane, then a dog cannot bark.

• A zebra has a mane and a dog can bark.

• A dog cannot bark or a zebra does not have a mane.

• A dog cannot bark if, and only if, a zebra does not have a mane.

Let p: D has a dog.

q: J has a cat.

Match each statement to the correct words.

• D has a dog and J has a cat.

• D has a dog or J has a cat.

• D doesn't have a dog if and only if J doesn't have a cat.

• J does not have a cat.

• If D doesn't have a dog, then J has a cat.

Let

• p: The temperature is 90°.

• q: The heater is working.

• r: The apartment is cold.

Match each statement to its symbolic form.

• The temperature is 90° and the heater is working, or the apartment is cold.

• If the temperature is 90°, then the heater is working or the apartment is not cold.

• If the temperature is not 90°, then the heater is working, and the apartment is cold.

• The temperature is 90° and the heater is not working, and the apartment is cold.

The Venn diagram represents groups of tradespersons.

Let p represent a tradesperson is a plumber.

Let q represent a tradesperson is a woodworker.

Let r represent a tradesperson is a carpenter.

Choose three conditional statements in if-then form describing

the relationships between the various groups of tradespersons.

• If a tradesperson is a carpenter, then they are a woodworker.

• If a tradesperson is a woodworker then they are a carpenter.

• If a tradesperson is a plumber then they are not a carpenter.

• If a tradesperson is a woodworker then they are not a plumber.

• If a tradesperson is a carpenter, then they are a plumber.