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Show that the square of an even number is an even number using direct proof
An=2*n+an-1,A1=1
1. Let p and q be propositions. p: You drive over 65 miles per hour. q: You get a speeding ticket. Write these propositions using p and q and logical connectives.
a. You do not drive over 65 miles per hour.
b. You will get a speeding ticket if you drive over 65 miles per hour.
c. If you do not drive over 65 miles per hour, then you will not get a speeding ticket.
In a large region, there are 450 farmers. 250 pounds of farm beetroot, 110 pounds of farm yams, 75 pounds of farm radish, 45 pounds of farm beetroot and radish, 40 pounds of farm yams and radish, and 30 pounds of farm beetroot and yams Let B, Y, and R represent the farms that grow beets, yams, and radish, respectively.
Determine the number of farmers that farm beetroot, yams, and radish.
Directions: Read each statement carefully, show your complete solution if needed.
1. Write out all functions f: (1,2,3) – (a,b) (using two
- line notation). How many Function are there? How many are surjective? How many are bijective?
2. For each function give below. Determine whether or not the function in injective and whether or not the function is surjective.
(a) f: N – N given by f(n) = n + 4
(b) f: Z – Z given by f(n) = n + 4
(c) f: Z – Z given by f(n) = 5n – 8
.Let A = {1, 2, 3, 4, 5} and B = {0, 3, 6}. Find a) A ∪ B. b) A ∩ B. c) A − B. d) B − A
Translate these statements into English, where C(x) is “x is a comedian” and F(x) is “x is funny” and the domain consists of all people.
a) ∀x(C(x) → F(x))
b) ∀x(C(x) ∧ F(x))
c) ∃x(C(x) → F(x))
d) ∃x(C(x) ∧ F(x))
Five thousand lottery tickets are sold for $1 each. One ticket will win $1000, two tickets will win $500 each, and ten tickets will win $100 each. Let X denote the net gain from the purchase of a randomly selected ticket.
a. Construct the probability distribution of C
b. Compute the standard deviation of X
Determine whether an Ex-OR or OR is needed for following propositions:
i. Coffee or tea comes with dinner.
ii. Experience with C++ or java is required.
iii. Lunch includes soup or salad.
Prove that ((𝑝 → 𝑞) ⋀ ¬𝑞 ) → ¬𝑝 ) it’s tautology without using truth table?
