Search & Filtering
Which of the following is false about a proposition?
(¬p ∨ p) is a proposition.(¬p ∧ p) is a proposition.A predicate is not a proposition.c.(¬p ∨ ¬p) is a proposition.
Let A be a given finite set and P(A) its power set. Let ⊆ be the inclusion relation on the elements of P(A). Draw Hasse diagrams of (P(A), ⊆) for A={a}; A={a,b}; A={a,b,c} and A={a,b.c.d}.
Consider the sequence (wn) defined recursively by
w2 = 3
wn = (wn-1 (1 - 0.02)) - 2(n + 1)/ n2 for n >= 3.
Write a MATLAB program to compute wn for n = 2, 3, 4, . . . , 10 and display the values n
and wn in two columns with appropriate headings. The program should also compute
and display the sum å10∑10\sum 10
∑10 i=2 wi
Showing all working, find a formula for the general term of the sequence (sn) = s3, s4, s5 . . . defined by
s3 = π and sn = sn-1 - 2 for n >= 4.
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
