116721
Suppose \(A, B\) and \(C\) are three sets, each with three elements. The number of subsets of the set \(A \times B \times C\) that have at least 2 elements is
1 \(\left(2^{27}\right)-28\)
2 \(\left(2^{27}\right)-55\)
3 27
4 \(\left(27^2\right)-3\)
Explanation:
A No of element in \(\mathrm{A} \times \mathrm{B} \times \mathrm{C}=3 \times 3 \times 3=27\) \(\therefore\) No. of subsets of the set \(\mathrm{A} \times \mathrm{B} \times \mathrm{C}=2^{27}\) No. of subsets having 1 element \(=27\) No. of subsets having 0 element \(=1\) So, required no. of subsets \(=2^{27}-(27+1)\) \(=2^{27}-28\)
J and K CET-2018
Sets, Relation and Function
116722
If \(P(A)=\frac{1}{4} ; P(B)=\frac{1}{5}\) and \(P(A B)=\frac{1}{8}\) then \(\mathbf{P}\left(\frac{\mathbf{A}^{\mathbf{C}}}{\mathbf{B}^{\mathbf{C}}}\right)=\)
116723
Suppose \(P, Q\) and \(R\) are three sets, each with three elements. The number of subsets of the set \(\mathbf{P} \times \mathbf{Q} \times \mathbf{R}\), that have at least 2 elements is
1 134217700
2 134217701
3 134217727
4 134217728
Explanation:
A Given, \(x(p)=3, x(Q)=3, x(R)=3\) So, total number of set \((\mathrm{x})=\mathrm{x}(\mathrm{p}) \times \mathrm{x}(\mathrm{Q}) \times \mathrm{x}(\mathrm{R})\) \(=3 \times 3 \times 3\) \(=27\) Total number of subset \(=2^x=2^{27}=134217728\) \(\therefore\) Number of subsets of the set that have at least 2 element \(=134217728-1-27\) \(=134217700\)
116721
Suppose \(A, B\) and \(C\) are three sets, each with three elements. The number of subsets of the set \(A \times B \times C\) that have at least 2 elements is
1 \(\left(2^{27}\right)-28\)
2 \(\left(2^{27}\right)-55\)
3 27
4 \(\left(27^2\right)-3\)
Explanation:
A No of element in \(\mathrm{A} \times \mathrm{B} \times \mathrm{C}=3 \times 3 \times 3=27\) \(\therefore\) No. of subsets of the set \(\mathrm{A} \times \mathrm{B} \times \mathrm{C}=2^{27}\) No. of subsets having 1 element \(=27\) No. of subsets having 0 element \(=1\) So, required no. of subsets \(=2^{27}-(27+1)\) \(=2^{27}-28\)
J and K CET-2018
Sets, Relation and Function
116722
If \(P(A)=\frac{1}{4} ; P(B)=\frac{1}{5}\) and \(P(A B)=\frac{1}{8}\) then \(\mathbf{P}\left(\frac{\mathbf{A}^{\mathbf{C}}}{\mathbf{B}^{\mathbf{C}}}\right)=\)
116723
Suppose \(P, Q\) and \(R\) are three sets, each with three elements. The number of subsets of the set \(\mathbf{P} \times \mathbf{Q} \times \mathbf{R}\), that have at least 2 elements is
1 134217700
2 134217701
3 134217727
4 134217728
Explanation:
A Given, \(x(p)=3, x(Q)=3, x(R)=3\) So, total number of set \((\mathrm{x})=\mathrm{x}(\mathrm{p}) \times \mathrm{x}(\mathrm{Q}) \times \mathrm{x}(\mathrm{R})\) \(=3 \times 3 \times 3\) \(=27\) Total number of subset \(=2^x=2^{27}=134217728\) \(\therefore\) Number of subsets of the set that have at least 2 element \(=134217728-1-27\) \(=134217700\)
116721
Suppose \(A, B\) and \(C\) are three sets, each with three elements. The number of subsets of the set \(A \times B \times C\) that have at least 2 elements is
1 \(\left(2^{27}\right)-28\)
2 \(\left(2^{27}\right)-55\)
3 27
4 \(\left(27^2\right)-3\)
Explanation:
A No of element in \(\mathrm{A} \times \mathrm{B} \times \mathrm{C}=3 \times 3 \times 3=27\) \(\therefore\) No. of subsets of the set \(\mathrm{A} \times \mathrm{B} \times \mathrm{C}=2^{27}\) No. of subsets having 1 element \(=27\) No. of subsets having 0 element \(=1\) So, required no. of subsets \(=2^{27}-(27+1)\) \(=2^{27}-28\)
J and K CET-2018
Sets, Relation and Function
116722
If \(P(A)=\frac{1}{4} ; P(B)=\frac{1}{5}\) and \(P(A B)=\frac{1}{8}\) then \(\mathbf{P}\left(\frac{\mathbf{A}^{\mathbf{C}}}{\mathbf{B}^{\mathbf{C}}}\right)=\)
116723
Suppose \(P, Q\) and \(R\) are three sets, each with three elements. The number of subsets of the set \(\mathbf{P} \times \mathbf{Q} \times \mathbf{R}\), that have at least 2 elements is
1 134217700
2 134217701
3 134217727
4 134217728
Explanation:
A Given, \(x(p)=3, x(Q)=3, x(R)=3\) So, total number of set \((\mathrm{x})=\mathrm{x}(\mathrm{p}) \times \mathrm{x}(\mathrm{Q}) \times \mathrm{x}(\mathrm{R})\) \(=3 \times 3 \times 3\) \(=27\) Total number of subset \(=2^x=2^{27}=134217728\) \(\therefore\) Number of subsets of the set that have at least 2 element \(=134217728-1-27\) \(=134217700\)
116721
Suppose \(A, B\) and \(C\) are three sets, each with three elements. The number of subsets of the set \(A \times B \times C\) that have at least 2 elements is
1 \(\left(2^{27}\right)-28\)
2 \(\left(2^{27}\right)-55\)
3 27
4 \(\left(27^2\right)-3\)
Explanation:
A No of element in \(\mathrm{A} \times \mathrm{B} \times \mathrm{C}=3 \times 3 \times 3=27\) \(\therefore\) No. of subsets of the set \(\mathrm{A} \times \mathrm{B} \times \mathrm{C}=2^{27}\) No. of subsets having 1 element \(=27\) No. of subsets having 0 element \(=1\) So, required no. of subsets \(=2^{27}-(27+1)\) \(=2^{27}-28\)
J and K CET-2018
Sets, Relation and Function
116722
If \(P(A)=\frac{1}{4} ; P(B)=\frac{1}{5}\) and \(P(A B)=\frac{1}{8}\) then \(\mathbf{P}\left(\frac{\mathbf{A}^{\mathbf{C}}}{\mathbf{B}^{\mathbf{C}}}\right)=\)
116723
Suppose \(P, Q\) and \(R\) are three sets, each with three elements. The number of subsets of the set \(\mathbf{P} \times \mathbf{Q} \times \mathbf{R}\), that have at least 2 elements is
1 134217700
2 134217701
3 134217727
4 134217728
Explanation:
A Given, \(x(p)=3, x(Q)=3, x(R)=3\) So, total number of set \((\mathrm{x})=\mathrm{x}(\mathrm{p}) \times \mathrm{x}(\mathrm{Q}) \times \mathrm{x}(\mathrm{R})\) \(=3 \times 3 \times 3\) \(=27\) Total number of subset \(=2^x=2^{27}=134217728\) \(\therefore\) Number of subsets of the set that have at least 2 element \(=134217728-1-27\) \(=134217700\)
