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 \[

Let A = {a, b, {c, d}, e} | False Statements in Sets Let A = {a, b, {c, d}, e} Let \[ A=\{a,b,\{c,d\},e\} \] Which of the following statements are false and why? (i) \(\{c,d\} \subset A\) (ii) \(\{c,d\} \in A\) (iii) \(\{\{c,d\}\} \subset A\) (iv) \(a \in A\) (v) \(a \subset A\) (vi)

Which of the Following Statements Are Correct? | Sets Class 11 Maths Solution Which of the Following Statements Are Correct? Which of the following statements are correct? Write a correct form of each of the incorrect statements. (i) \(a \subset \{a,b,c\}\) (ii) \(\{a\} \in \{a,b,c\}\) (iii) \(a \in \{\{a\},b\}\) (iv) \(\{a\} \subset \{\{a\},b\}\) (v) \(\{b,c\}

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