Prove That X ⊆ Y for X = {8ⁿ − 7n − 1} and Y = {49(n − 1)} Prove That X ⊆ Y If \[ X=\{8^n-7n-1:n \in N\} \] and \[ Y=\{49(n-1):n \in N\} \] then prove that \[ X \subseteq Y \] Solution Let \[ x=8^n-7n-1 \] where \[ n \in N \] […]

Find the Universal Set for Right Triangles and Isosceles Triangles Find the Universal Set for Right Triangles and Isosceles Triangles What universal set(s) would you propose for each of the following: (i) The set of right triangles. (ii) The set of isosceles triangles. Solution (i) A suitable universal set for the set of right triangles

How Many Elements Has P(A), if A = Φ? | Sets Class 11 Maths How Many Elements Has P(A), if A = Φ? How many elements has \[ P(A) \] if \[ A=\Phi \] ? Solution Since \[ A=\Phi \] there are \[ 0 \] elements in \[ A \] Number of elements in \[

Prove That A ⊆ B, B ⊆ C and C ⊆ A iff A = C | Sets Prove That A ⊆ B, B ⊆ C and C ⊆ A iff A = C Prove that \[ A \subseteq B,\ B \subseteq C \text{ and } C \subseteq A \iff A=C \] Solution Given \[

Prove That A ⊆ Φ iff A = Φ | Sets Class 11 Maths Prove That A ⊆ Φ iff A = Φ If \[ A \] is any set, prove that \[ A \subseteq \Phi \iff A=\Phi \] Solution If \[ A \subseteq \Phi \] then every element of \[ A \] belongs to

Total Number of Proper Subsets of a Set Having n Elements Total Number of Proper Subsets of a Set Having n Elements What is the total number of proper subsets of a set consisting of \[ n \] elements? Solution A set having \[ n \] elements has \[ 2^n \] subsets. A proper subset

Write Down All Possible Proper Subsets of Given Sets | Sets Class 11 Maths Write Down All Possible Proper Subsets of Given Sets Write down all possible proper subsets of each of the following sets: (i) \(\{1,2\}\) (ii) \(\{1,2,3\}\) (iii) \(\{1\}\) Solution (i) Proper subsets of \[ \{1,2\} \] are \[ \Phi,\ \{1\},\ \{2\} \]

Write Down All Possible Subsets of Given Sets | Sets Class 11 Maths Write Down All Possible Subsets of Given Sets Write down all possible subsets of each of the following sets: (i) \(\{a\}\) (ii) \(\{0,1\}\) (iii) \(\{a,b,c\}\) (iv) \(\{1,\{1\}\}\) (v) \(\{\Phi\}\) Solution (i) Subsets of \[ \{a\} \] are \[ \Phi,\ \{a\} \] (ii)

Let A = {0, {Φ}, 1, {1, Φ}, 2} | True or False in Sets Let A = {0, {Φ}, 1, {1, Φ}, 2} Let \[ A=\{0,\{\Phi\},1,\{1,\Phi\},2\} \] Which of the following are true? (i) \(\Phi \in A\) (ii) \(\{\Phi\} \in A\) (iii) \(\{1\} \in A\) (iv) \(\{2,0\} \subset A\) (v) \(2 \subset A\) (vi)

Let A = {{1,2,3},{4,5},{6,7,8}} | True or False in Sets Let A = {{1,2,3},{4,5},{6,7,8}} Let \[ A=\{\{1,2,3\},\{4,5\},\{6,7,8\}\} \] Determine which of the following is true or false: (i) \(1 \in A\) (ii) \(\{1,2,3\} \subset A\) (iii) \(\{6,7,8\} \in A\) (iv) \(\{\{4,5\}\} \subset A\) (v) \(\Phi \in A\) (vi) \(\Phi \subset A\) Solution Elements of \[