Show solution.

a. How many natural numbers between 1 and 6000 (inclusive) are divisible by 2,

3 0r 5?

b. How many integers between 1 and 200, including both 1 and 200, are divisible

by 4 or 5?

c. How many integers between 1 and 21,000, including both 1 and 21,000, are

divisible by 2, 3 or 7 but not 5?

Symbolize the following by using quantifiers, predicates, and logical

connectives. (Note: You have to assign variables for predicates and

subjects on your own.)

a. All rational numbers are real numbers.

b. Some rational numbers are integers.

c. Some even numbers are multiple two.

d. Some triangles are scalene.

e. Every integer is multiple of 10 if and only if it is a multiple of 5 and 2.

f. Some prime integers are odd integers.

g. Everyone is charitable and compassionate.

h. Some are committed and competent in doing their job.

i. Everyone who studies logic is good in reasoning.

j. Some students are good in Mathematics and Physics.