Answer the following questions
Write the following statements in symbolic form
(a) Milk is white if and only if the sky is not blue
(b) If Kutab - Minar is in Delhi then Taj - Mahal is in Agra
(c) Even though it is not cloudy, it is still raining

Answer

To convert the given statements into symbolic form, we will define some variables to represent the propositions involved. Let's denote:

- Let \( p \): "Milk is white"
- Let \( q \): "The sky is blue"
- Let \( r \): "Qutub Minar is in Delhi"
- Let \( s \): "Taj Mahal is in Agra"
- Let \( t \): "It is cloudy"
- Let \( u \): "It is raining"

Now, we can express each statement in symbolic form:

### (a) Milk is white if and only if the sky is not blue.

1. The statement "the sky is not blue" can be represented as \( \neg q \).
2. The phrase "if and only if" indicates a biconditional relationship, which can be represented as \( p \iff \neg q \).

**Symbolic Form**:
\[ p \iff \neg q \]

### (b) If Qutub Minar is in Delhi then Taj Mahal is in Agra.

1. The statement "Qutub Minar is in Delhi" can be represented as \( r \).
2. The statement "Taj Mahal is in Agra" can be represented as \( s \).
3. The phrase "if... then..." indicates an implication, which can be represented as \( r \implies s \).

**Symbolic Form**:
\[ r \implies s \]

### (c) Even though it is not cloudy, it is still raining.

1. The statement "it is not cloudy" can be represented as \( \neg t \).
2. The statement "it is still raining" can be represented as \( u \).
3. The phrase "even though" indicates a conjunction, which can be represented as \( \neg t \land u \).

**Symbolic Form**:
\[ \neg t \land u \]

### Summary of Symbolic Forms:
- (a) \( p \iff \neg q \)
- (b) \( r \implies s \)
- (c) \( \neg t \land u \)