9th Class Mathematics Unit 3 Sets and Functions Numericals with Solutions

3.1.1.Write the following sets in set builder notation: (i) {1, 4, 9, 16, 25, 36, ..., 484} (ii) {2, 4, 8, 16, ..., 256} (iii) {0, ±1, ±2, ..., ±1000} (iv) {6, 12, 18, ..., 120} (v) {100, 102, 104, ..., 400} (vi) {1, 3, 9, 27, 81, ...} (vii) {1, 2, 4, 5, 10, 20, 25, 50, 100} (viii) {5, 10, 15, ..., 100} (ix) The set of all integers between -100 and 1000

Result

(i) {xmid x=n², nin N wedge 1le nle 22}

(ii) {xmid x=2ⁿ, nin N wedge 1le nle 8}

(iii) {xmid xin Z wedge -1000le xle 1000}

(iv) {xmid x=6n, nin N wedge 1le nle 20}

(v) {xmid x=100+2n, nin W wedge 0le nle 150}

(vi) {xmid x=3ⁿ, nin W}

(vii) {xmid x is a divisor of 100}

(viii) {xmid x=5n, nin N wedge 1le nle 20}

(ix) {xmid xin Z wedge -100< x< 1000}

3.1.2.Write each of the following sets in tabular forms: (i) {x|x is a multiple of 3 ∧ x≤36} (ii) {x|x∈R∧2x+1=0} (iii) {x|x∈P∧x<12} (iv) {x|x is a divisor of 128} (v) {x|x=2^n,n∈N∧n<8} (vi) {x|x∈N∧x+4=0} (vii) {x|x∈N∧x=x} (viii) {x|x∈Z∧3x+1=0}

Result

(i) {3,6,9,dots,36}

(ii) left{-12right}

(iii) {2,3,5,7,11}

(iv) {1,2,4,8,16,32,64,128}

(v) {2,4,8,16,32,64,128}

(vi) { }

(vii) {1,2,3,4,5,dots}

(viii) { }

3.1.3.Write two proper subsets of each of the following sets: (i) {a,b,c} (ii) {0,1} (iii) N (iv) Z (v) Q (vi) R (vii) {x|x∈Q∧0<x≤2}

Result

(i) {a}, {b}

(ii) {0}, {1}

(iii) {1}, {2}

(iv) {1}, {2}

(v) {1}, {2}

(vi) {1}, {2}

(vii) {1}, {2}

3.1.4.Is there any set which has no proper subset? If so, name that set.

Result

Yes, { } or varphi

3.1.5.What is the difference between {a, b} and {{a,b}}?

Result

{a,b} has two elements a,b; {{a,b}} has one element, the set {a,b}

3.1.6.What is the number of elements of the power set of each of the following sets? (i) {} (ii) {0,1} (iii) {1,2,3,4,5,6,7} (iv) {0,1,2,3,4,5,6,7} (v) {a,{b,c}} (vi) {{a,b},{b,c},{d,e}}

Result

(i) 1

(ii) 4

(iii) 128

(iv) 256

(v) 4

(vi) 8

3.1.7.Write down the power set of each of the following sets: (i) {9,11} (ii) {+,-,×,÷} (iii) {φ} (iv) {a,{b,c}}

Result

(i) {varphi,{9},{11},{9,11}}

(ii) {varphi,{+},{-},{ × },{div},{+,-},{+, × },{+,div},{-, × },{-,div},{ × ,div},{+,-, × },{+,-,div},{+, × ,div},{-, × ,div},{+,-, × ,div}}

(iii) {varphi,{varphi}}

(iv) {varphi,{a},{{b,c}},{a,{b,c}}}

Unit 3: Sets and Functions — Exercise 3 1