Question

Write down the negations of the following expressions, so that the symbol does not arise to the left of any quantifier. Indicate whether the negated statement is true a) Vx E N, x2 e N and - eN 2x b) Vx E R,3n E Z, x" < 0.

Please provide explanation to each step as I need to study for exam. I will upvote. Thanks!

Answer 1

a) VxEN, EN and N The above statement is True The Negation statement taue Must Apply Negabtion and 4N) EN 7ANELT TATR%eN) 7Cand) 7 N)) 7and ov E EAL eN, xN pormula's TAENE AAN eN OV 2 7 x s natuval Not natuttlval number ik Here 2 7 number Value of EN it is impotsible 4N for any palse False False OY false statement Proved as Tt is negated Atatemunt Conect Since onginal satement 1rue Negated statement false so ouv

2)eR, anez , "20 / Contains vand statement Heve the statement and Bome and 3 statemint true me false and its negattonae to all ituations it a stalements a statement cant be true 1 determined negation pituakions original true definitely talre APPY negatron 10ER, gne 2, " 20) xER, VnE2 , x" >o Negation Atatemnt and 2 et not O but negation stafement . . Dt s po ved as covrect