## Question

###### 4.18. Prove the proposition Vx â‚¬ R, Vy â‚¬ R, 3z â‚¬ R,(x - 2)2 < (x y)?. 4.19. Prove the proposition Vx â‚¬ R, Jy,z â‚¬ R, y2 < x2 < 22 4.20. Disprove the proposition Vx â‚¬ N, Jy eN,y < x. 4.21. Disprove the proposition Ix â‚¬ N; Vy â‚¬ N,y < x. 4.22. Prove or disprove the proposition Vx â‚¬ N, Jy â‚¬ N, X <y < (x +1)2. 4.23. Prove OT disprove the proposition Vx e %, Vy â‚¬ Z, 3ez, (x < y) - (x < 2 < y). 4.24. Prove Ot disprove the proposition Vx â‚¬ R, Vy â‚¬ R

4.18. Prove the proposition Vx â‚¬ R, Vy â‚¬ R, 3z â‚¬ R,(x - 2)2 < (x y)?. 4.19. Prove the proposition Vx â‚¬ R, Jy,z â‚¬ R, y2 < x2 < 22 4.20. Disprove the proposition Vx â‚¬ N, Jy eN,y < x. 4.21. Disprove the proposition Ix â‚¬ N; Vy â‚¬ N,y < x. 4.22. Prove or disprove the proposition Vx â‚¬ N, Jy â‚¬ N, X <y < (x +1)2. 4.23. Prove OT disprove the proposition Vx e %, Vy â‚¬ Z, 3ez, (x < y) - (x < 2 < y). 4.24. Prove Ot disprove the proposition Vx â‚¬ R, Vy â‚¬ R, 3z â‚¬ R, (x < y) + (x < 2 < y): 59

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