Let X be a set of $$5$$ elements. The number d of ordered pairs (A, B) of subsets of X such that $$A\neq \Phi, B\neq \Phi, A\cap B=\Phi$$ satisfies.
Total no. of ordered pairs is
$${ =C }_{ 2 }^{ 5 }\times 2!+{ C }_{ 3 }^{ 5 }\left( \frac { 3! }{ 1!\times 2! } \times 2! \right) +{ C }_{ 4 }^{ 5 }\left( \frac { 4! }{ 1!\times 3! } \times 2!+\frac { 4! }{ 2!\times 2! } \times \frac { 2! }{ 2! } \right) +{ C }_{ 5 }^{ 5 }\left( \frac { 5! }{ 1!\times 4! } \times 2!+\frac { 5! }{ 2!\times 3! } \times 2! \right) \\ =10(2)+10(6)+5(8+6)(10+20)\\ =180\\ $$
So option $$C$$ is correct
State true or false. Given universal set= $$\displaystyle =\left \{ -6,-5\frac{3}{4}, -\sqrt{4}, -\frac{3}{5}, -\frac{3}{8}, 0, \frac{4}{5}, 1, 1\frac{2}{3}, \sqrt{8}, 3.01, \pi , 8.47 \right \}$$ From the given set, the set of integers is $$\displaystyle \left \{ -6,-\sqrt{4}, 0,1 \right \}$$.
State true or false. Given universal set= $$\displaystyle =\left \{ -6,-5\frac{3}{4}, -\sqrt{4}, -\frac{3}{5}, -\frac{3}{8}, 0, \frac{4}{5}, 1, 1\frac{2}{3}, \sqrt{8}, 3.01, \pi , 8.47 \right \}$$ From the given set, find set of non-negative integers is $$\displaystyle \left \{0,1 \right \}$$.
State true or false: A set of rational number is a subset of a set of real numbers.
What universal set (s) would you propose for each of the following: The set of isosceles triangles.
Let $$A, B$$ and $$C$$ be sets such that $$\phi = A\cap B \subseteq C$$. Then which of the following statements is not true?
Given a non empty set X, consider $$P(X)$$ which is set of all subsets of $$X$$. Define the relation $$R$$ is $$P(X)$$ as follows: For subsets $$A, B$$ in $$P(X), ARB$$ if and only if $$A\subset B$$. Is R an equivalence relation on $$P(X)$$? Justify your answer
For any set $$A$$, if $$A\subseteq \phi \Leftrightarrow A=\phi$$.
Examine whether the following statements are true or false: $$(a,b)\not{\subset}(b,c,a)$$
Examine whether the following statements are true or false: $$(a,e) \subset$$ ($$x : x$$ is a vowel in the English alphabet)
Examine whether the following statements are true or false: $$(1,2,3)\subset (1,3,5)$$