Negate the following statement:

If 𝐚=1 and 𝐛=2, then 𝐚+𝐛=3.

The given statement is:  
**"If 𝑎 = 1 and 𝑏 = 2, then 𝑎 + 𝑏 = 3."**

To negate this statement, we need to use the principle of negating an implication. The original statement is of the form:
\[ P \implies Q \]
where:
- \( P \): "𝑎 = 1 and 𝑏 = 2"
- \( Q \): "𝑎 + 𝑏 = 3"

The negation of \( P \implies Q \) is:
\[ P \land \neg Q \]
which translates to:
- \( P \): "𝑎 = 1 and 𝑏 = 2" (stays true)
- \( \neg Q \): "𝑎 + 𝑏 \neq 3"

Thus, the negated statement is:
**"𝑎 = 1 and 𝑏 = 2, and 𝑎 + 𝑏 ≠ 3."**

Would you like further details or have any questions about negation?

Here are five related questions to deepen understanding:
1. How do you negate a universal quantifier?
2. What is the negation of "If it rains, then the ground is wet"?
3. How do logical operators like "and" and "or" behave under negation?
4. Can you provide an example of a negated conjunction?
5. What happens when you negate a biconditional statement?

**Tip:** When negating an implication, the "if" part remains true, but the "then" part must be false.

Negate the following statement: If a = 1 and b = 2, then a + b = 3.

Learn how to negate the logical implication 'If a = 1 and b = 2, then a + b = 3.' This problem introduces key logical concepts such as negation and implication, and is suitable for students in Grades 10-12 studying logic.

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