Discrete Mathematics Answers

Find the power set of each of these sets, where a and b are distinct elements. a) {a} b) {a, b} c) {∅,{∅}}

Evaluate the truth value of the following propositions using the set (1 ,3, 5, 7)

as the domain.

1. Vx: x (x2 – 4) = 0

2. Ǝx : x + 1 > 0

3. Ǝx : x (x2

– 4) = 0

Translate the following into symbolic

form and give its domain.

1. All fishes are swimmers.

2. Some fruits are sweet.

3. Every number is a real number.

4. Any mammal is not two-legged.

1.    The encrypted version of a message is DSWO PYB PEX. If it was encrypted using the function f(p) = (p + 10) mod 26 (the Caesar cipher), what was the original message?

1.    Use the Euclidean algorithm to find the greatest common divisor (gcd) of each pairs of integers. Show the steps of calculation.

a) (900,140)                                                                                                         

b) (128,729)

If p and q are two propositions, then show that ~ (p V q) Ξ ~ p ~ q

Let P(x):x2/2=x

Find the following then identify their truth values.

P (1)

P (2)

∀n,P(n)

∃n,P (n)

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.

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.

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.