Subsets and supersets - class-VIII

$\text{Clearly, set A contain all elements of set C}$
$\Rightarrow \text{A is superset of C}$

We need subsets {a, b} from {1, ..., 10} where min(a, b) < 6. If min is 1, there are 9 choices for the other number. If min is 2, there are 8 choices. If min is 3, there are 7. If min is 4, there are 6. If min is 5, there are 5. Sum = 9+8+7+6+5 = 35.

We know that $\mathbb{N} \subset \mathbb{Z}$ where $\mathbb{N}$ represents set of natural numbers and $\mathbb{Z}$ represents set of all positive and negative integers.

Since $\mathbb{N} \subset \mathbb{Z}$,

                                 $(a),(b),(c)$ are subsets of $(e)$        $...(1)$

Since $\mathbb{Z}$ represents set of all positive and negative integers.

                                      $(d)$ is a subset of $(e)$                   $...(2)$

From $(1)$ and $(2)$ we get

$(a),(b),(c),(d)$ are subsets of $(e)$.

Hence $(e)$ is the universal set for the other four sets.

We have to state whether the statement "$0 \in \phi$" is true or false.

We know that, $\phi$ represents null set.

The null set, also called the empty set, is the set that does not contain any element.

Thus by the definition of null set, $0 \notin \phi$

Hence the given statement is false.