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Why is f not a function from R to R if
a) f (x) = 1/x?
b) f (x) =√x?
c) f (x) = ±√(x^2+1)?
Check whether the compound proposition
(p ∨￢q) ∧(q ∨￢r) ∧(r ∨￢p) ∧(p ∨q ∨r) ∧(￢p ∨￢q ∨￢r)
is satisfiable or not?
find 200 sum k=100^k
3a²n−1
1. Show if satisfy the algebraic axioms:
identity and inverse under addition.
2. Show if satisfy all (communicative, associative, identity, and inverse) the algebraic axioms under both multiplication and addition.
3. Which number set can you find the inverse of integers under multiplication?
4. Which number set can you find the inverse of natural numbers under multiplication?
5. Find the prime factors of the following numbers:
(a) 2003
(b) 1560
(c) 5680
(d) 3050
6. Calculate gcd of the following using Euclidean Algorithm:
(a) (572, 279)
(b) (138, 114)
(c) (578, 255)
(d) (688, 212)
1. Is the function 𝑓: ℤ → ℤ 𝑓(𝑥) = 𝑥 2 + 3 injective, surjective or bijective? Prove your assertions
Provethat12 +32 +52 +⋯+(2n+1)2 = (n+1)(2n+1)(2n + 3)∕3 whenever n is a nonnegative integer.
Find a formula for
1+1+⋯+ 1
1 ⋅ 2 2 ⋅ 3 n(n + 1)
by examining the values of this expression for small
values of n.
b) Prove the formula you conjectured in part
Question 6 (6 marks)
6a) Draw the Venn diagrams for each of these combinations of the sets A, B, and C: (i) (A – C)C ⋂ ( B- C)C (3 marks)
(ii) (A – C) U (C – B)(3 marks)
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