MATH 2090  Problem Set #2 (On Ch.11)

York University

Faculties of Pure and Applied Science, Arts, Atkinson MATH 2090. Problem Set #1. Posted January 27, 2002 Due in the Course Box. Friday, February 8, 2002

Section N

In your proofs it is imperative to clearly state what tools you use (e.g., WLUS, SLCS, MP, PSL,

Monotonicity, Deduction Theorem, Weak Generalization, which axiom(s), etc.)

From the text p.213–215: Do the set(!) of problems

{11.3, 11.4, 11.7(d), 11.12((a)–(c)), 11.13(d), 11.15, 11.17}

Conventions AND notation from class apply! In particular, 1. Convert GS-assertions to “standard notation” before you start your proof.

2. Note that we have only one set theory axiom, Extensionality. Also do

• Prove ST ⊢ (∀a, b, c, d)({{a}, {a, b}} = {{c}, {c, d}} ⇒ a = c ∧ b = d).

• ST ⊢ A ⊂ B ⇒ (∃x)(x ∉ A).

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