Fundamentals of Math

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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