Given:
The product of a particular number is 65.
Second value is given by the sum of 8 and the original number.
To find:
The unknown number.
Solution:
Let x be the unknown number.
Then, second number = x+8
The product of a particular number is 65.
Splitting the middle term, we get
Using zero product property, we get
and
and
So, the unknown number is either 5 or -13.
Therefore, the correct option is B.
Answer:
Remember, if B is a set, R is a relation in B and a is related with b (aRb or (a,b))
1. R is reflexive if for each element a∈B, aRa.
2. R is symmetric if satisfies that if aRb then bRa.
3. R is transitive if satisfies that if aRb and bRc then aRc.
Then, our set B is .
a) We need to find a relation R reflexive and transitive that contain the relation
Then, we need:
1. That 1R1, 2R2, 3R3, 4R4 to the relation be reflexive and,
2. Observe that
Therefore is the smallest relation containing the relation R1.
b) We need a new relation symmetric and transitive, then
and the analysis for be transitive is the same that we did in a).
Observe that
Therefore, the smallest relation containing R1 that is symmetric and transitive is
c) We need a new relation reflexive, symmetric and transitive containing R1.
For be reflexive
For be symmetric
For be transitive
Then, the smallest relation reflexive, symmetric and transitive containing R1 is