Discrete Mathematics Answers

There are 60 science students tn a

Secondary School. 35 of whom study

Chemistry and 30 study Technical

Drawing, 12 out of those students atudy

Biology and chemistry but not Technical

Drawing, 10 study Chemistry but

neither biology nor Technical Drawing 11

study only Technical Drawing and

neither Biology nor Chemistry, 10 also

study Chemistry and Technical Drawing

only

a. How many mdents study all the three

subjects?

b. How many students study biology and

Technical Drawing but not Chemistry?

C. How many students study Biology only?

d How many students study biology all

together.

p: "I study for the test"

q: "I am sick"

r: "I fail the exam"

Translate the compound proposition below into words:

(¬p∨q)→r

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