Question

Which statement is an example of a transitive relationship? If x = 2y and 2y = 8, then x = 4. If m ⊥ n and m ⊥ p, then m ∥​ p. If ℓ ⊥ m and m ∥ n, then ℓ ⊥ n. If a ∥ b and b ∥ c, then a ∥ c.

Answer 1

the answer is if a || b and b || c, then a || c.

Explanation:

"If x = 2y and 2y = 8, then x = 4" this is wrong because 4 and 8 don't equal each other, and "If m ⊥ n and m ⊥ p, then m ∥​ p. If ℓ ⊥ m and m ∥ n, then ℓ ⊥ n" is wrong because lines that are parallel, cannot intersect. a transitive relationship is when 3 variables are connected and shown as, for example "A = b, and b = c, then A=C

Answer 2

Answer with explanation:

The relationship is said to be transitive, if

a R b, b R c, then → a R c.

Option 1:

x=2 y, and , 2 y =8

Then for transitive relationship, x=8.

The given statement, x=4 , is incorrect statement from the point of view of transitive relationship.

Option 2:

If m ⊥ n and m ⊥ p, then m ∥​ p.

Incorrect statement from the point of view of transitive relationship.

it should be, n ⊥ p.

Option 3:

If ℓ ⊥ m and m ∥ n, then ℓ ⊥ n.

There must be same sign or relation between , ℓ , m and n.

Incorrect statement from the point of view of transitive relationship.

Option 4:

If a ∥ b and b ∥ c, then a ∥ c.

a R b , means , a is parallel to B.

b R c , means b is parallel to c.

a R c, means , a is parallel to c.

There is same relation(R), called Parallelism between , a , b and c.

So,this is transitive relationship.

Option 4: is an example of transitive relationship.