Show that a b = ∅ → a ⊆ b[hints(1 x ε a → x

Info iconThis preview shows pages 3–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Show that A - B = ∅ → A ⊆ B. [Hints: (1) x ε A → x ∉ ∅ → ... . (2) A - B = ∅ → ∀ x( x ε A - B → x ε ∅ ). The contrapositive of the implication within the parentheses here is useful in dealing with the ellipsis in hint #1.] _________________________________________________________________ 9. (5 pts.) If f:X → Y is a function, f-1 may be used to denote two quite different things. What are they? [Use complete sentences.] TEST1/MAD2104 Page 4 of 4 _________________________________________________________________ 10. (15 pts.) Suppose that f: → Ζ is the function defined by the formula f(x)= x , and suppose that A = {x ε | -3 ≤ x ≤ 3} and B = {x ε | -1 < x ≤ π }. Using appropriate notation, give each of the following. A - B = f(B) = f-1 ({1,3}) = _________________________________________________________________ 11. (5 pts.) What is the value of the following sum of terms of a geometric progression? [Hint: You may wish to re-index the varmint.] 8 ∑ 2 j = j=1 _________________________________________________________________ 12. (5 pts.) Suppose g:A → B and f:B → C are functions. Prove exactly one of the following propositions. Indicate clearly which you are demonstrating. (a) If f g:A → C is injective, then g is injective. (b) If f g:A → C is surjective, then f is surjective....
View Full Document

{[ snackBarMessage ]}

Page3 / 4

Show that A B = ∅ → A ⊆ B[Hints(1 x ε A → x ∉...

This preview shows document pages 3 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online