Solution: Let's say A, B and C are the set of people who like product A, product B and product C respectively. So now, as per the question, n (A) = 21 be Number of students who like product A, n (B)...
Solution: (i) Let's suppose that, The set of people who read newspaper H = A The set of people who read newspaper T = B The set of people who read newspaper I = C As per the question, $n (A) = 25$ =...
Solution: Let's suppose that, The set of all students in the group be U The set of students who know English be E $\therefore \mathrm{H} \cup \mathrm{E}=\mathrm{U}$ Provided that, $n(H)=100$ =...
Solution: Let's suppose that, The set of all students who took part in the survey be U The set of students taking tea be T The set of the students taking coffee be C Therefore, the total number of...
Solution: Let's suppose, $A\{0,1\}$ $B=\{1,2\}$ And, $C=\{2,0\}$ As per the question, $A \cap B=\{1\}$ $B \cap C=\{2\}$ And, $A \cap C=\{0\}$ $\therefore A \cap B, B \cap C$ and $A \cap C$ are not...
Solution: As per the question, Let's say $A$ and $B$ are two sets such that $A \cap X=B \cap X=\phi$ and $A \cup X=B \cup X$ for some set $X$ We need to show, $A=B$ Proof: $\begin{array}{l} A=A...
Solution: Let's suppose, $\begin{array}{l} A=\{0,1\} \\ B=\{0,2,3\} \end{array}$ And, $C=\{0,4,5\}$ As per the question, $A \cap B=\{0\}$ And, $\begin{array}{l} A \cap C=\{0\} \\ \therefore A \cap...
Solution: (i) We need to show: $A \cup(A \cap B)=A$ As it is known that, $\begin{array}{l} A \subset A \\ A \cap B \subset A \\ \therefore A \cup(A \cap B) \subset A..........(i) \end{array}$ Also,...
Solution: We need to Prove, $A=(A \cap B) \cup(A-B)$ Proof: Let $x \in A$ We need to show $X \in(A \cap B) \cup(A-B)$ In Case I, $X \in(A \cap B)$ $\Rightarrow X \in(A \cap B) \subset(A \cup B)...
Solution: We need to show, $A=B$ As per the question, $P(A)=P(B)$ Let's say $x$ is any element of set $A$, $x \in A$ As, $P(A)$ is the power set of set $A$, it has all the subsets of set $A$. $A \in...
Solution: We need to show, $C-B \subset C-A$ As per the question, Let's suppose that $x$ is any element such that $X \in C-B$ $\therefore x \in C$ and $x \notin B$ As, $A \subset B$, we get,...
Solution: As per the question, We need to prove, $(i) \mapsto$ (ii) Given here, $(i)=A \subset B$ and $(i i)=A-B \neq \phi$ Let's suppose that $A \subset B$ We need to prove, $A-B \neq \phi$ Let's...
Solution: As per the question, $A \cup B=A \cup C$ And, $A \cap B=A \cap C$ We need to show that, $B=C$ Let's suppose, $x \in B$ Therefore, $\begin{array}{l} x \in A \cup B \\ x \in A \cup C...
Solution: (i) The statement is false As per the question, $x \in A$ And also, $A \not \subset B$ Let's suppose that, $A=\{3,5,7\}$ Also here, $B=\{3,4,6\}$ It is known that, $A \not \subset B$...
Solution: (i) The statement is true As per the question $A \subset B$ and $B \subset C$ Let's suppose that, $x \in A$ Therefore, we have, $x \in B$ And $x \in C$ As a result, $A \subset C$ (ii) The...
Solution: (i) The statement is false As per the question, $A\text{ }=\text{ }\left\{ 1,\text{ }2 \right\}$ and $B\text{ }=\text{ }\left\{ 1,\text{ }\left\{ 1,\text{ }2 \right\},\text{ }\left\{ 3...
}, B = {2, 4, 6}, C = {2, 4, 6, 8…}, D = {6}.Solution: As per the question, A $=$ {x: x ∈ R and x satisfies $x2 {-} 8x + 12 =0$} The only solutions of $x2 {-} 8x + 12 = 0$ are 2 and 6. As a result, A $=$ {2, 6} B $=$ {2, 4, 6}, C $=$ {2, 4, 6,...