Results for query "Suppose $p(x"

attaching maps in CW complexes

Suppose I have a finite CW complex $X$ with $p$-skeleton $X^{(p)}$.Suppose that the map $\theta = q_e \circ \varphi_f \colon S^p \to X^{(p)} \to S^p$ is surjective.

Predicates and Quantifiers

a) ∀x(A → P(x)) ≡ A → ∀xP(x)

b) ∃x(A → P(x)) ≡ A → ∃xP(x)

My Solution

a) Suppose A is false.Then A -> P(x) is trivially true because if hypothesis is false then conditional statement is trivially true.