Write Which of the Following Statements Are True | Sets Class 11 Maths Solution Write Which of the Following Statements Are True Write which of the following statements are true? Justify your answer. (i) The set of all integers is contained in the set of all rational numbers. (ii) The set of all crows is […]

Decide Which Sets Are Subsets of Which | Sets Class 11 Maths Solution Decide Which Sets Are Subsets of Which Decide among the following sets, which are subsets of which: \[ A=\{x:x \text{ satisfies } x^2-8x+12=0\} \] \[ B=\{2,4,6\} \] \[ C=\{2,4,6,8,\ldots\} \] \[ D=\{6\} \] Solution First solve \[ x^2-8x+12=0 \] \[ x^2-6x-2x+12=0 \]

State Whether the Following Statements Are True or False | Sets Class 11 Maths State Whether the Following Statements Are True or False State whether the following statements are true or false: (i) \(1 \in \{1,2,3\}\) (ii) \(a \subset \{b,c,a\}\) (iii) \((a) \in \{a,b,c\}\) (iv) \(\{a,b\}=\{a,a,b,b,a\}\) (v) The set \[ \{x:x+8=8\} \] is the null

Which of the Following Statements Are True? | Sets Class 11 Maths Solution Which of the Following Statements Are True? Which of the following statements are true? Give reason to support your answer. (i) For any two sets \(A\) and \(B\) either \(A \subseteq B\) or \(B \subseteq A\). (ii) Every subset of an infinite

Show That the Sets of Letters in “CATARACT” and “TRACT” are Equal Show That the Sets of Letters in “CATARACT” and “TRACT” are Equal Show that the set of letters needed to spell “CATARACT” and the set of letters needed to spell “TRACT” are equal. Solution The set of letters in the word “CATARACT” is

Which of the Following Sets are Equal? Which of the Following Sets are Equal? Set Roster Form \[ A=\{x:x\in N,\ x

Equal Sets and Equivalent Sets Equal Sets and Equivalent Sets Set Number of Elements \[ A=\{0,a\} \] 2 \[ B=\{1,2,3,4\} \] 4 \[ C=\{4,8,12\} \] 3 \[ D=\{3,1,2,4\} \] 4 \[ E=\{1,0\} \] 2 \[ F=\{8,4,12\} \] 3 \[ G=\{1,5,7,11\} \] 4 \[ H=\{a,b\} \] 2 Equal Sets Sets having exactly the same elements are

Are the Following Pairs of Sets Equal? Are the Following Pairs of Sets Equal? Question Answer (i) \[ A=\{2,3\} \] \[ B=\{x:x \text{ is a solution of }x^2+5x+6=0\} \] \[ x^2+5x+6=0 \] \[ (x+2)(x+3)=0 \] \[ x=-2,-3 \] Therefore, \[ B=\{-2,-3\} \] Since \[ A=\{2,3\}\ne\{-2,-3\}, \] the sets are not equal. (ii) \[ A=\{x:x \text{

Pair the Equivalent Sets Pair the Equivalent Sets Set Number of Elements \[ A=\{1,2,3\} \] 3 \[ B=\{t,p,q,r,s\} \] 5 \[ C=\{\alpha,\beta,\gamma\} \] 3 \[ D=\{a,e,i,o,u\} \] 5 Conclusion Equivalent sets have the same number of elements. Since \[ n(A)=n(C)=3, \] therefore \[ A \sim C \] Also, \[ n(B)=n(D)=5, \] therefore \[ B \sim

Are the Following Sets Equal? Are the Following Sets Equal? Set Roster Form \[ A=\{x:x \text{ is a letter in the word “reap”}\} \] \[ A=\{r,e,a,p\} \] \[ B=\{x:x \text{ is a letter in the word “paper”}\} \] \[ B=\{p,a,e,r\} \] \[ C=\{x:x \text{ is a letter in the word “rope”}\} \] \[ C=\{r,o,p,e\} \]