Question

3. Let A-1,2,3,43 B-(3,4,5,63 C (5,6,73 a. b. c. What is A n B? What is A n C? Translate the following q E Q a, b E Z Э q

Answer 1

A={1,2,3,4}

B={3,4,5,6}

C={5,6,7}

(a) A $\cap$ B is a set containing common points of set A and set B.

A $\cap$ B = {3,4}

(b) A $\cap$ C ={}

It is a null set meaning there are no common elements in sets A and C.

(c) $\mathbb{Z}$ denotes a set o integers

$\mathbb{Q}$ denotes a set of Rational numbers

a $\in$ A means a belongs to set A (small letters are elements capitals are sets)

P $\ni$ a is just opposite to above means a belongs to set P (only working difference is order is from right to left in this case)

$\forall$ means for all

$\exists$ means exists or there exists.

Given notation translates to

For all elements q belonging to set of Rational numbers, there exists a and b elememts belonging to the set of Integers (means a and b are integers) and q which is equal to a divided by b also belongs to integers.

In simpler language it says for any rational number q it is equal ratio(fraction) of two integers a and b. However, they also need to add that b ≠ 0. Otherwise it will not be defined.