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Which of the following sentences are pro...

Which of the following sentences are propositions ? What are the truth values of those that are propositions (statement)?
(i) Do you speak Hindi ? (ii) Four is even.
(iii) Please submit your proposal as soon as possible.
(iv) Do you speak English ?
(v) 4 - x= 8.
(vi) Please try to solve the problem.

Text Solution

AI Generated Solution

The correct Answer is:
To determine which of the given sentences are propositions, we will analyze each sentence based on the definition of a proposition. A proposition is defined as a statement that can either be true or false, but not both at the same time. ### Step-by-Step Solution: 1. **Sentence (i): "Do you speak Hindi?"** - This is a question and does not have a definitive true or false value. Therefore, it is **not a proposition**. 2. **Sentence (ii): "Four is even."** - This is a declarative statement that can be evaluated as true (since 4 is indeed an even number). Therefore, it is a **proposition** with a truth value of **true**. 3. **Sentence (iii): "Please submit your proposal as soon as possible."** - This is a request and does not have a truth value (it cannot be classified as true or false). Therefore, it is **not a proposition**. 4. **Sentence (iv): "Do you speak English?"** - Similar to the first sentence, this is a question and does not have a definitive true or false value. Therefore, it is **not a proposition**. 5. **Sentence (v): "4 - x = 8."** - This is an equation that can be true or false depending on the value of x. Since it does not have a fixed truth value, it is **not a proposition**. 6. **Sentence (vi): "Please try to solve the problem."** - This is also a request and does not have a truth value. Therefore, it is **not a proposition**. ### Summary of Propositions: - The only proposition among the sentences is: - (ii) "Four is even." with a truth value of **true**. ### Final Answer: - Propositions: (ii) "Four is even." - Truth Value: True
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