List All the Elements of the Following Sets List All the Elements of the Following Sets Set Elements (i) \[ A=\{x:x^2\le10,\ x\in Z\} \] \[ A=\{-3,-2,-1,0,1,2,3\} \] (ii) \[ B=\left\{x:x=\frac1{2n-1},\ 1\le n\le5\right\} \] \[ B=\left\{1,\frac13,\frac15,\frac17,\frac19\right\} \] (iii) \[ C=\left\{x:x\text{ is an integer},\ -\frac12

Describe the Following Sets in Set-Builder Form Describe the Following Sets in Set-Builder Form Roster Form Set-Builder Form \[ A=\{1,2,3,4,5,6\} \] \[ A=\{x\in N:1\le x\le6\} \] \[ B=\left\{1,\frac12,\frac13,\frac14,\frac15,\ldots\right\} \] \[ B=\left\{x:x=\frac1n,\ n\in N\right\} \] \[ C=\{0,3,6,9,12,\ldots\} \] \[ C=\{x:x=3n,\ n\in W\} \] \[ D=\{10,11,12,13,14,15\} \] \[ D=\{x\in N:10\le x\le15\} \] \[ E=\{0\} \] \[ E=\{x:x=0\}

Describe the Following Sets in Roster Form Describe the Following Sets in Roster Form Question Roster Form (i) \[ \{x:x \text{ is a letter before e in the English alphabet}\} \] \[ \{a,b,c,d\} \] (ii) \[ \{x\in N:x^2

Insert the Appropriate Symbol ∈ or ∉ Insert the Appropriate Symbol ∈ or ∉ If \[ A=\{0,1,2,3,4,5,6,7,8,9,10\}, \] then insert the appropriate symbol \[ \in \text{ or } \notin \] in each of the following. Question Answer i. \(4\ …\ A\) \[ 4 \in A \] ii. \(-4\ …\ A\) \[ -4 \notin A \]

Which of the Following Collections are Sets? Which of the Following Collections are Sets? Collection Set / Not a Set Reason (i) A collection of all natural numbers less than 50. Set The collection is well-defined. (ii) The collection of good hockey players in India. Not a Set The word “good” is not well-defined. (iii)

Difference Between a Collection and a Set Difference Between a Collection and a Set What is the difference between a collection and a set? Give reasons to support your answer. Solution Collection Set A collection is simply a group of objects. A set is a well-defined collection of distinct objects. A collection may or may

Assertion and Reason on {(0.027)³ + (0.023)³}/{(0.027)² − (0.027)(0.023) + (0.023)²} Assertion and Reason Question on Algebraic Identities Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. (a) Statement-1 is true, Statement-2 is true; Statement-2

Assertion and Reason on a²/bc + b²/ca + c²/ab = 3 Assertion and Reason Question on Algebraic Identities Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. (a) Statement-1 is true, Statement-2 is true; Statement-2

Assertion and Reason on a³ + b³ + c³ − 3abc Assertion and Reason Question on Algebraic Identities Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. (a) Statement-1 is true, Statement-2 is true; Statement-2

Assertion and Reason on If 3x = a + b + c Then (x − a)³ + (x − b)³ + (x − c)³ = 3(x − a)(x − b)(x − c) Assertion and Reason Question on Algebraic Identities Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices