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3 years ago

7

Determine whether the given relation is reflexive, symmetric, transitive, or none of these. Justify your answers.Recall that a p

rime number is an integer that is greater than 1 and has no positive integer divisors other than 1 and itself. (In particular, 1 is not prime.) A relation P is defined on ℤ as follows:For every m, n is in ℤ, m P n ⇔ ∃ a prime number p such that p | m and p | n.

1 answer:

OlgaM077 [116]3 years ago

7 0

Answer:

Is Reflexive.

Is Symmetric

Is NOT transitive

Step-by-step explanation:

Is Reflexive.

Because any integer $n$ is divided by some prime $p$ . Since $p | n , p|n$ it is true that $n P n$

Is Symmetric

Suppose that $n P m$ then there is a $p$ such that $p|n , \,\, p|m$ , then $p|m , \,\, p|n$ and $m P n$ .

Is NOT transitive

Notice that $3P6$ and $6P8$ , but 3 is NOT related to 8 because no prime divide both numbers.

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What is the measurement of angle POR

IgorLugansk [536]

Let us observe the given figure,

When two lines intersect each other, the angles opposite to each other are Vertically Opposite Angles. Vertically opposite angles are always equal in measure.

As, we can observe that the given lines intersect each other, and they form vertically opposite angles as $\angle POR , \angle SOQ$ and $\angle POS , \angle ROQ$

Therefore, $\angle POR = \angle SOQ$

Substituting the given measures of the angles, we get

$91-x^\circ = x+ 7^\circ$

$91-7 = x + x$

$84 = 2x$

$x = \frac{84}{2}$

So, x = $42^\circ$

Since, the measure of angle POR = $(91-x)^\circ$

= $(91-42)^\circ$

= $49^\circ$

Therefore, the measure of angle POR is 49 degrees.

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4 years ago

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