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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.

Respuesta :

batolisis

Answer:

a) True

b) True

c) True

d) True

e) False

f) False

Step-by-step 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

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