Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack. a) {(a, b) | a and b are the same age}
b) {(a, b) | a and b have the same parents}
c) {(a, b) | a and b share a common parent}
d) {(a, b) | a and b have met}
e) {(a, b) | a and b speak a common language}

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Secant be and cf intersect at point d inside a what is the measure of cde

The graph of f(x) = |x| is transformed to g(x) = |x + 11| - 7. on which interval is the function decreasing?