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.

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

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

       F          T        T

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

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

D)  3 ∈ Z and 3 ∈ Q

where p =  3 ∈ Z   and q = 3 ∈ Q

E)  2 / 3 ∈ Z and 2 / 3 ∈ Q

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

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

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

where is the triangle?

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq