Search & Filtering
How many ways are there to select 12 countries in the United Nations to serve on a council if 3 is selected from a block of 53, 1 are selected from a block of 62 and 8 are selected from the remaining 74 countries?
Construct a truth table for each of these compound propositions.
(i) (p → q) ↔ (¬q → ¬p) (16 marks)
ii) p ⊕ (p ∨ q) (8 marks)
(i) Determine by using truth tables if (p ∧ q) → p is a tautology, contradiction or a contingency. Give reasons for your answer. (6 marks)
(ii) Show that ¬(p ⊕ q) and p ↔ q are logically equivalent. (6 marks)
Let the universe of discourse be the set of all integers. Let p; q; r; s, and t be as follows: p(x):x>0,q(x):xiseven,r(x):xisaperfectsquare,s(x):xis(exactly)divisibleby4, t(x):x is (exactly) divisible by 5. (8 marks)
Write the following statements using quantifiers and logical connectives
i. At least one integer is even.
ii. There exists a positive integer that is even.
iii. If x is even, then x is not divisible by 5.
iv. There exists an even integer divisible by 5.
Given A = {x | x ∈ Z- ∧ 3x > -10}. Determine elements of A.
Let A, B and C denotes the subset of a set, S and let 𝐶̅denotes the complement of C in set S.
If (A ∩ C) = (B ∩ C) and (A ∩ 𝐶̅) = (B ∩ 𝐶̅), then prove that (A = B).
Determine the domain of each of the following functions: 1. f(x) = x + 10 6. A(x) = x2 -2 2. F(x) = 2 3 𝑥 + 5 7. H(x) = √𝑥 − 2 3. g(x) = 5 – 3x 8. K(x) = √𝑥 2 − 2 4. g(x) = 1 (𝑥+5)(𝑥−1) 9. C(x) = 2x3 + 4x2 - 2x + 1 5. b(x) = 𝑥−1 𝑥 2+5𝑥+6 10. √𝑥+1 𝑥−2
B. Exercises: Let f(x) = x – 3 , g(x) = 2x + 1 and h(x) = x2 – 5. Find the following 1. f ₒ g 2. f ₒ h 3. h ₒ g 4. g ₒ f 5. g ₒ h
Let f(x) = x – 3 , g(x) = 2x + 1 and h(x) = x2 – 5. Find the following 1. f ₒ g 2. f ₒ h 3. h ₒ g 4. g ₒ f 5. g ₒ h
1. Find a relation R such that 𝑥+𝑦 2 >1 if A = {0,1, 2} and B ={0, 1, 2, 3}.
A. Try these! 1. Find a relation R such that 𝑥+𝑦 2 >1 if A = {0,1, 2} and B ={0, 1, 2, 3}. 2. Find a relation R such that y is a power of x if A = {1, 2, 3} and B = {1, 4, 5, 9}
