Fundamentals of Math - old

Fundamentals of Mathematics

Example 8.1

Write each of the following sentence combinations as outlined below and determine if the combined statement is true or false.

Let be "Dylan owns a bed" and is true, and let be "Dylan owns a pillow," which is also true.

1.

∧ Recall, ∧ is the symbol for a conjunction which means "and"

3.

→ Recall, → the symbol for conditional, which is "if-then"

Dylan owns a bed, and Dylan owns a pillow.

If Dylan owns a bed, then Dylan owns a pillow.

∧ T

→

T

T

T

T

T

2.

∨ Recall, ∨ is the symbol for a disjunction which means "or"

4.

⟷ Recall, ↔ is the symbol for biconditionals "if-and-only-if"

Dylan owns a bed, or Dylan owns a pillow.

Dylan owns a bed if and only if Dylan owns a pillow.

∨ T

T

T

⟷

T

T

T

Practice 8.1

Directions: Let p be "The car is black" and let q be "The car has a heated steering wheel". Represent each of the follow sentences using the logical operations of and ( ∧ ), or ( ∨ ), not (~), if/then ( → ), and if and only if ( ⟷ ) and exclusive or (~).

1. The car is not black and the car does not have a heated steering wheel. 2. The car is not black and the car has a heated steering wheel. 3. The car is black and the car has a heated steering wheel. 4. The car is black and the car does not have a heated steering wheel.

Using the statements above, fill in the truth table with all possible combinations of and .

Statement 1

Statement 2

Statement 3

Statement 4

T T F F

T F T F

Answer Key on Page 125

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