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Let p, q, and r be the propositions. p : You get an A on the final exam. q : You do every exercise in this book. r : You get an A in this class. Write these propositions using p, q, and r and logical connectives (including negations). Then, Construct the truth table of the each proposition a) You get an A in this class, but you do not do every exercise in this book. b) You get an A on the final, but you do every exercise in this book, and you get an A in this class. c) You will get an A in this class if and only if you either do every exercise in this book or you get an A on the final. d) You get an A on the final, but you don’t do every exercise in this book; nevertheless, you get an A in this class.
If 11 students offer Biology, 13 students offer Maths, 14 students offer Agric, 9 students offer Maths and Biology, 3 students offer Maths and Agric, 7 students offer Maths, Biology and Agric. How many students offer Biology and Agric?
2-2.7+2.7^2-...+2(-7)^n = (1- (-7)^n+1)/4
I. p is "x< 50"; q is "x> 40".
Express the following compound propositions as English sentences in as natural a way as you can
(a) ¬p
(b) ¬q
(d) p∨q
(e) ¬pV q
(f) ¬pV ¬q
Find the power set of the set {Ø , { Ø }, a, b, c} where a, b and c are distinct elements.
Express each of the statements using quantifiers. Then form the negation of the statement, so that no negation is to the left of a quantifier. Next, express the negation in simple English. (Do not simply use the words “It is not the case that”).
Some dogs can learn new tricks.
No rabbit knows calculus.
Every bird can fly.
There is no dog that can talk.
There is no one in this tutorial who knows Irish and Russian
Use bit strings to find the union, intersection, A and B compliments of these sets. The bit strings for the sets {2, 3, 6, 7 and 8} and {1, 3, 5, 7, 9} are 0110011100 and 1010101010, respectively.
If A is a set, let A¯ denote the complement of A. Show the following (a) (A ∩ B¯) ⊂ A ∩ B (b) A − B = A if and only if B − A = B
Let S denote the set of all companies listed on the Botswana Stock Exchange. Define the following sets as: A = x | x is in the mining sector , B = x | x has an annual turnover exceeding P10 million , C = x | x has a financial year ending in June , D = x | x share price is higher now than six months ago . Describe in words the following sets: (a) A ∪ B (b) B ∩ C (c) B ∩ (C ∪ A) (d) (B ∩ A) ∪ (C ∩ D)
Write the sequence of the following explicit formula.
1. sn = (-4)^n, 1 ≤ n
2. bn = 92 - 5n, 1 ≤ n ≤ 5
3. Blue taxi inc. charges $7.50 for the first 4 miles and 1 dollar for each additional miles. The table shows the cost of travelling from 4 to 10 miles.
mileage 4, cost 7.50
mileage 5, cost 8.50
mileage 6, cost 9.50
mileage 7, cost 10.50
mileage 8, cost 11. 50
mileage 9, cost 12.50
mileage 10, cost 13. 50
Write the recursive formula.
Write the explicit formula
4. If the sequence formula is given as tn = n^2 -1, n less than or equal to 1.
Write the first five terms of the sequence
Write the 55th term
