Question

For each of the following propositions, identify simple propositions, express the compound proposition in symbolic form, and determine whether it is true or false: The world is flat or zero is an even integer. If 432,802 is a multiple of 4, then 432,802 is even. 5 is a prime number and 6 is not divisible by 4. 3 ∈ Z and 3 ∈ Q . 2 / 3 ∈ Z and 2 / 3 ∈ Q . The sum of two even integers is even and the sum of two odd integers is odd.

Answer 1

a) True

b) True

c) True

d) True

e) False

f) False

Explanation:

a) The world is flat or Zero is an even Integer

• simple proposition : it is a compound interest

• expressing compound proposition in symbolic form : p v q ; where p = world is flat and q = Zero is an integer

• It is a true statement

B ) If 432,802 is a multiple of 4, then 432,802 is even

• simple proposition : It is a compound statement

• expressing compound proposition in symbolic form : p ⇒ q ; where p = 432,802 is a multiple of 4 and q = 432,802 is even

• p q p ⇒ q hence statement is true

F T T

C) 5 is a prime number and 6 is not divisible by 4

• simple proposition : it is a compound statement

• symbolic form ; p ∧ q

where p = 5 is a prime number and q = 6 is not divisible by 4

• statement is true

D) 3 ∈ Z and 3 ∈ Q

• simple proposition : it is a compound statement

• symbolic form : p ∧ q

where p = 3 ∈ Z and q = 3 ∈ Q

• statement is true

E) 2 / 3 ∈ Z and 2 / 3 ∈ Q

• simple proposition : It is a compound statement

• symbolic form : p ∧ q

where p = 2 / 3 ∈ Z ( false ) and q = 2 / 3 ∈ Q ( true ) hence p ∧ q = false

• statement is false

F) The sum of two even integers is even and the sum of two odd integers is odd.

• simple proposition : It is a compound statement

• symbolic form : p ∧ q

where p = The sum of two even integers is even and q = the sum of two odd integers is odd.

• statement is false