Chapter 1 - Section 1.4 - Predicates and Quantifiers - Exercises - Page 55: 35

a) No counterexample b) x=0 c) x=2

a) $\forall x (x^{2}\geq x)$ No counter example because x^2 (since x is an integer) will always be greater x. b)$\forall x (x>0 \lor x<0)$ Counter example is x = 0; 0>0 or 0<0 is false c) $\forall x (x=1)$ Counter example is x = 2; 2=1 is false.