GATE Overflow Test Series | Discrete Mathematics | Test 1 | Question: 8

Question

Which of the following is a valid partition for $N,$ where $N$ is the set of natural numbers? (Mark all the appropriate choices)

• A. $\{x \in N \mid x \geq 100 \} \cup \{x \in N \mid x \leq 100\}$
• B. $\{x \in N \mid x \geq 100 \} \cup \{x \in N \mid x < 100\}$
• C. $\{x \in N \mid x > 100 \} \cup \{x \in N \mid x < 100\}$
• D. $\{x \in N \mid x \geq 101 \} \cup \{x \in N \mid x < 100 \}$

Answer 1

$\pi$ is a partition of A if

1.  $|A_i| \geq 1$
2.  $A_i \cap A_j = \phi \ \forall A_i,A_j \in \pi$
3. $\bigcup A_i = A$

Only option B is satisfying all the properties of a partition set.
In option A, $100$ is common in both sets
In option C, $100$ is missing in both the sets
In option D, $100$ is missing in both the sets

Comments

yes

---

In option D 100 is missing that is why we did not choose it ? 

@Deepak Poonia sir 

---

@Harshit Dubey, Yes. 

Answer 2

Only B true as it includes 100 uniquely.