Answer:
Option A.
Step-by-step explanation:
step 1
we know that
The equation of the solid line is
The solution is the shaded area above the solid line
so
The equation of the first inequality is
step 2
The equation of the dashed line is
The solution is the shaded area above the dashed line
so
The equation of the second inequality is
therefore
The system of inequalities could be
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