Question

Consider the sets : X = set of all students in your school, Y = set of all students in your class. We note that every element of Y is also an element of X; we say that Y is a subset of X. The fact that Y is subset of X is expressed in symbols as Y ⊂ X. The symbol ⊂ stands for ‘is a subset of’ or ‘is contained in’. In other words, A ⊂ B if whenever a ∈ A, then a ∈ B. It is often convenient to use the symbol “⇒” which means implies. Using this symbol, we can write the definition of subset as follows: A ⊂ B if a ∈ A ⇒ a ∈ B Using this information answer the following questions 1.1 Let A={{1}, 2,3} then find which of the following is NOT CORRECT option (a){1} ⊂ (b) 2 ∈ (c ) {2,3} ⊂ (d) 3 ∈ 1.2 Let A={{1}, 2,3} then IMPROPER subset of A is (a){1} (b) {1,2,3} (c) ∅ (d) {2,3} 1.3 Let a, b ∈ and < then express the subset of real numbers {x : a ≤ x < b}in interval form (a) [,] (b) [, ) (c) (, ) (d) (, ] 1.4 For any finite set A={, , } we represent the power set by P(A) , then find number of elements in the set P(A) (a)3 (b) 6 (c) 9 (d) 8 1.5 The set P{P(∅)] can be expressed as , where ∅ is null set (a)∅ (b) {∅} (c){∅,{∅}} (d) { }​

Answer 1

Answer:

The answer 50x 67y

Step-by-step explanation:

Hope it helps you

Answer 2

1.1 Let A={{1}, 2,3} then find which of the following is NOT CORRECT option

(a){1} ⊂ (b) 2 ∈ (c ) {2,3} ⊂ (d) 3 ∈

(a) {1} ⊂ A is the incorrect answer.

We can see that {1} is an element of A therefore {1}  ∈ A will be the correct symbol.

1.2 Let A={{1}, 2,3} then the IMPROPER subset of A is

(a){1} (b) {1,2,3} (c) ∅ (d) {2,3}

(c) ∅ is the correct answer.

None of the given options is an improper subset of A. An improper subset is the one that contains all the elements of the other subset and we can see there is no option like that.

1.3 Let a, b ∈ and < then express the subset of real numbers {x : a ≤ x < b}in interval form

(a) [,] (b) [, ) (c) (, ) (d) (, ]

(b) [, ) will be the correct answer.

We can see from the question that a ≤ x < b therefore on the left-hand side we will have a square bracket while on the right-hand side we will have a simple parenthesis.

1.4 For any finite set A={, , } we represent the power set by P(A), then find the number of elements in the set P(A)

(a)3 (b) 6 (c) 9 (d) 8

(a)3  Will be the correct answer.

We know that all the elements inside a set are separated by a ',' so we have 2 ',' in this set therefore there will be 3 elements inside the set.

1.5 The set P{P(∅)] can be expressed a, where ∅ is a null set

(a)∅ (b) {∅} (c){∅,{∅}} (d) { }​

(a) ∅ will be the correct answer.

A null set is always expressed by the '∅' symbol and there is no need of adding brackets.