Fill in the blanks.

(i) $A' \cap \phi = $ ___
(ii) $A \cap \phi' = $ ___
(iii) $A \cup U' = $ ___
(iv) $A \cap U' = $ ___
(v) $A \cap \phi' = $ ___
(vi) $U' \cap \phi = $ ___
(vii) $U' \cap \phi' = $ ___
(viii) $U' \cup \phi = $ ___
(ix) $U' \cup \phi' = $ ___
(x) $U \cup \phi'

Question

Fill in the blanks.

(i) $A' \cap \phi = $ ___
(ii) $A \cap \phi' = $ ___
(iii) $A \cup U' = $ ___
(iv) $A \cap U' = $ ___
(v) $A \cap \phi' = $ ___
(vi) $U' \cap \phi = $ ___
(vii) $U' \cap \phi' = $ ___
(viii) $U' \cup \phi = $ ___
(ix) $U' \cup \phi' = $ ___
(x) $U \cup \phi' = $ ___

Accepted Answer

> [!TLDR]
> Since $U' = \phi$ (complement of the universal set is empty) and $\phi' = U$ (complement of the empty set is the universal set), substitute and apply the identity laws $A\cap U = A$, $A\cup \phi = A$, $A\cap\phi=\phi$, $A\cup U = U$.

> [!FORMULA]
> Identity laws: $A\cup\phi = A$, $A\cap U = A$, $A\cap\phi = \phi$, $A\cup U = U$. Complement of universal/empty set: $U' = \phi$, $\phi' = U$.

1. **(i) $A'\cap\phi$:** intersection with the empty set is always empty. $= \phi$.

2. **(ii) $A\cap\phi'$:** since $\phi' = U$, this is $A\cap U = A$.

3. **(iii) $A\cup U'$:** since $U' = \phi$, this is $A\cup\phi = A$.

4. **(iv) $A\cap U'$:** since $U' = \phi$, this is $A\cap\phi = \phi$.

5. **(v) $A\cap\phi'$:** same as step 2 — $\phi'=U$, so $A\cap U = A$.

6. **(vi) $U'\cap\phi$:** $U'=\phi$, so this is $\phi\cap\phi = \phi$. …

Q.Fill in the blanks.

Concept understanding — Types of Sets

Types of Sets — From Intuition to Precision

1. The Empty Set (Null Set)

2. Finite and Infinite Sets

3. Equal Sets

4. Subsets and Supersets

5. Universal Set

6. Power Set …

Q.Fill in the blanks.

🎓Unlock everything free for 14 days

Unlock everything free for 14 days