Answer
a. There exists a real number (x) that when added to any real number (y) results in the value of that real number (y).
b.The difference of any non-negative real number and any negative real number is positive.
c.There exist two non-positive real numbers whose difference is positive.
d. For every two real numbers, the two real numbers are both non-zero if and only if their product is non-zero.
Work Step by Step
a. $\exists$ means THERE EXISTS and $\forall $ means FOR EVERY
There exists a real number (x) that when added to any real number (y) results in the value of that real number (y).
b.$\exists$ means THERE EXISTS and $\rightarrow$ means IF-THEN
$\geq 0$ means non-negative
$>0$ means positive
$<0$ means negative
The difference of any non-negative real number and any negative real number is positive.
c.$\exists$ means THERE EXISTS and $\land$ means AND
$\leq0$ means non-positive
$>0$ means positive
There exist two non-positive real numbers whose difference is positive.
d. $\forall $ means FOR EVERY and $\land$ means AND and $\leftrightarrow$ means IF AND ONLY IF
For every two real numbers, the two real numbers are both non-zero if and only if their product is non-zero.
