Chapter 3.3, Problem 12ES

a.

To determine

To find: Whether the statement “ ${\forall }_x$ in $D$ , ${\exists }_y$ in $E$ , such that $x+y=1$ ” is true or its negation.

b.

To determine

To find: Whether the statement is “ ${\exists }_x$ in $D$ such that ${\forall }_y$ in $E$ , $x+y=-y$ ” true or its negation.

c.

To determine

To find: Whether the statement “ ${\forall }_x$ in $D$ , ${\exists }_y$ in $E$ , such that $xy\ge y$ ” is true or its negation.

d.

To determine

To find: Whether the statement “ ${\exists }_x$ in $D$ such that ${\forall }_y$ in $E$ , $x\le y$ ” is true or its negation.