0 votes 0 votes Find a counterexample, if possible, to these universally quantified statements, where the domain for all variables consists of all integers. a) ∀x∃y(x = 1/y) b) ∀x∃y(y^2 − x < 100) Mathematical Logic discrete-mathematics propositional-logic mathematical-logic engineering-mathematics kenneth-rosen + – ykrishnay asked Apr 19, 2022 ykrishnay 312 views answer comment Share Follow See 1 comment See all 1 1 comment reply shishir__roy commented Apr 19, 2022 i edited by shishir__roy Apr 19, 2022 reply Follow Share x, y $\in$ Z a) Any x such that x $\neq$ 1 $\land$ x $\neq$ -1, is a counter example for statement a. y = 1 / x, y $\notin$ Z for x $\neq$ 1, -1 b) Any x such that x < -100, is a counter example for statement b. y^2 - x < 100 $\implies$ y < $\sqrt{100+x}$, y $\notin$ Z for x < 100 1 votes 1 votes Please log in or register to add a comment.