Solution 2.3 -《Sets, Functions, and Logic》

2.3 a)

  1. (a) (∃x∈N)(x3=27)
    (b) (∃p∈N)(p>1,000,000)
    (c) ∃((p∈N)∧(1<p<n))np∈N

  2. (a) (∀x∈N)(x3≠8)
    (b) (∀p∈N)(0<p)
    (c) ∀((p∈N)∧(1<p<n))np∈N

  3. (a) For all the people, it is the case that there exists someone they love:
    (∀x∈people)(∃y∈people)(x loves y)
    (b) (∀x∈people)(x is tall) or (∀x∈people)(x is short)
    (c) (∀x∈people)((x is tall) or (x is short))
    (d) (∀x∈people)(x is not at home)
    (e) (∀x∈men)(∀y∈women)(x comes and y leaves)

  4. (a) (∀a∈R)(∃x∈R)(x2+a=0)
    (b) ((∀a∈R)∧(a<0))(∃x∈R)(x2+a=0)
    (c) ∀x∈R,∃p,q∈N such that x=pq
    (d) ∃x∈R such that ∀p,q∈N,x≠p2q
    (e) ((∀x∈R)(∀p,q∈N)(x≠pq))(∀y∈N)(∀m,n∈N)(y≠mn)(y>x)

(a) (∀D(x))(M(x))
b) (∀¬D(x))(M(x))
c) (∀M(x))(D(x))
d) (∃D(x))(¬M(x))
e) (∃¬D(x))(M(x))

∀(x,y∈R)∧((x<x)∨(y<x))(∃x∈R)(Q(x))

(A or B)∧(C)

(((∃x∈people)(∀t∈time)(You fool x with t time))∨((∃t∈time)(∀y∈people)(You fool y with t time)))∧¬(∀x∈people)(∀t∈time)(You fool x with t time)

posted @   马路野狼  阅读(8)  评论(0)  编辑  收藏  举报
相关博文：
· Solution 2.2 -《Sets, Functions, and Logic》
· First-Order Conditions For Convexity
· P8773 题解
· P2757题解
· 每日导数43
阅读排行：
· 【自荐】一款简洁、开源的在线白板工具 Drawnix
· 没有Manus邀请码？试试免邀请码的MGX或者开源的OpenManus吧
· 无需6万激活码！GitHub神秘组织3小时极速复刻Manus，手把手教你使用OpenManus搭建本
· C#/.NET/.NET Core优秀项目和框架2025年2月简报
· DeepSeek在M芯片Mac上本地化部署
点击右上角即可分享
微信分享提示
主题色彩