Question

2. For the following quantified statement, (a) Write the negation of the statement. (Don't simply put a in front of the statement. Actually rewrite to get a quantified statement that is equivalent to the negation.) Original Statement: Vr e Z. By e Z, az eZ: 72 = y2 + z2. Negation of the original statement: (b) Decide whether the original statement is true or the negation of the original statement is true. Include some brief justification of how you know.

Answer 1

..2) (a) Original statement in the Zt; FYEZ, J ZEZ :22=42+22 - Negation is :- FREZ, &YEL, VZE2 : x² #4722 . (b). Original statement is false Take x=3. Then there is no y, z in i satisfying .x²=4²+ 2.2 ..