The truth table represents statements p, q, and r. p q r a t t t b t t f c t f t d t f f e f t t f f t f g f f t h f f f which statements are true for rows a and e? check all that apply. p ↔ q p ↔ r q ↔ p q ↔ r r ↔ p r ↔ q

We have been given the truth table for three variables p, q, and r. as shown below

p q r

A T T T

B T T F

C T F T

D T F F

E F T T

F F T F

G F F T

H F F F

Now we need to find Which statements are true for rows A and E for the following statements:

p ↔ q p ↔ r q ↔ p q ↔ r r ↔ p r ↔ q

To find that we need to use table of P <-> Q as shown in picture.

We know that if both statements are true for P and Q then only P <-> Q will be true. So using that trick we see that only q<->r and r<->q are the final answer as shown in the attached picture.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.