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Which of the following expressions are s...

Which of the following expressions are statements ,
(i) `1+2+3= 1xx2xx3` (ii) `{2, 3} sub {2, 4, 6}`
(iii) May you live long. (iv) 7 is a prime number
(v) `5 in {1, 4, 5)` (vi) All roses are white
(vii) What is your Name?
(viii) The girls are beautiful.
(ix) Go to your home.
(x) Blood is red.

Text Solution

AI Generated Solution

The correct Answer is:
To determine which of the given expressions are statements, we will analyze each expression based on the definition of a statement in mathematical reasoning. A statement is defined as an expression that can be either true or false, but not both at the same time. ### Step-by-Step Solution: 1. **Expression (i): `1 + 2 + 3 = 1 × 2 × 3`** - Calculation: Left side = 1 + 2 + 3 = 6; Right side = 1 × 2 × 3 = 6. - Conclusion: Both sides are equal (6 = 6), so this expression is **true**. - **Statement**: Yes. 2. **Expression (ii): `{2, 3} ⊆ {2, 4, 6}`** - Analysis: The set {2, 3} is a subset of {2, 4, 6} if all elements of {2, 3} are in {2, 4, 6}. - Conclusion: 3 is not in {2, 4, 6}, so this expression is **false**. - **Statement**: Yes. 3. **Expression (iii): "May you live long."** - Analysis: This is a wish or hope and does not have a truth value (neither true nor false). - **Statement**: No. 4. **Expression (iv): "7 is a prime number."** - Analysis: This is a factual statement that can be evaluated. - Conclusion: 7 is indeed a prime number, so this expression is **true**. - **Statement**: Yes. 5. **Expression (v): `5 ∈ {1, 4, 5}`** - Analysis: This expression checks if 5 is an element of the set {1, 4, 5}. - Conclusion: 5 is in the set, so this expression is **true**. - **Statement**: Yes. 6. **Expression (vi): "All roses are white."** - Analysis: This is a general statement that can be evaluated but is factually incorrect (not all roses are white). - Conclusion: This expression is **false**. - **Statement**: Yes. 7. **Expression (vii): "What is your name?"** - Analysis: This is a question and does not have a truth value. - **Statement**: No. 8. **Expression (viii): "The girls are beautiful."** - Analysis: This is a subjective statement and can be interpreted as true or false based on opinion. - Conclusion: It does not have a definitive truth value. - **Statement**: No. 9. **Expression (ix): "Go to your home."** - Analysis: This is a command and does not have a truth value. - **Statement**: No. 10. **Expression (x): "Blood is red."** - Analysis: This is a factual statement that can be evaluated. - Conclusion: Generally, blood is red, so this expression is **true**. - **Statement**: Yes. ### Summary of Statements: - **Statements**: (i), (ii), (iv), (v), (vi), (x) - **Not Statements**: (iii), (vii), (viii), (ix)
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