For each of the following determine whether the relation on the given set is reflexive, symmetric, transitive, and an equivalence relation (where ⇐⇒ means if and only if). Justify each of your answers (with proof or counterexamples).

1. R={(f, g)|f(1)=g(1)}on the set A={f|f:Z→Z}
2. R={(f, g)|f(0)=g(0)or f(1)=g(1)}on set A={f|f:Z→Z}
3. ((a, b),(c, d))∈R⇐⇒a+d=b+c on A=Z×Z
4. xRy⇐⇒x−y ∈ Z on A=R

45

step-by-step explanation:

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.

answer: answer: d) v= 1/6 bh  

step-by-step explanation:

since according to the given question,   a pyramid is placed inside a prism.

step-by-step explanation:

none of these

step-by-step explanation:

23 + 34 add up to 57 so just inform the teacher of this really stupid mistake