Write the negations of the following statements :
(1) Some continuous functions are differentiable.
(2) All parents care of their children.
(3) `EEx""inR` such that `x^(2)ltx`
(4) `AAninN,x^(2)+x` is even number.
(5) It is neither cold nor raining.
(6) If n is an even number, then 2n is not divisible by 4.
(7) A triangle is an equilateral if and only if it is an equiangular triangle.
(8) If I drive fast and do not follow traffic rules, then I will meet with an accident.

Answer

Let's break down the negation of each statement step by step:

### Step 1: Negation of "Some continuous functions are differentiable."
- Original Statement: "Some continuous functions are differentiable."
- Negation: "All continuous functions are not differentiable."

### Step 2: Negation of "All parents care for their children."
- Original Statement: "All parents care for their children."
- Negation: "Some parents do not care for their children."

### Step 3: Negation of "There exists x in R such that x^2 < x."
- Original Statement: "There exists x in R such that x^2 < x."
- Negation: "For all x in R, x^2 ≥ x."

### Step 4: Negation of "For all n in N, x^2 + x is an even number."
- Original Statement: "For all n in N, x^2 + x is an even number."
- Negation: "There exists n in N such that x^2 + x is not an even number."

### Step 5: Negation of "It is neither cold nor raining."
- Original Statement: "It is neither cold nor raining."
- Negation: "It is cold or it is raining."

### Step 6: Negation of "If n is an even number, then 2n is not divisible by 4."
- Original Statement: "If n is an even number, then 2n is not divisible by 4."
- Negation: "n is an even number and 2n is divisible by 4."

### Step 7: Negation of "A triangle is equilateral if and only if it is equiangular."
- Original Statement: "A triangle is equilateral if and only if it is equiangular."
- Negation: "A triangle is equilateral and it is not equiangular."

### Step 8: Negation of "If I drive fast and do not follow traffic rules, then I will meet with an accident."
- Original Statement: "If I drive fast and do not follow traffic rules, then I will meet with an accident."
- Negation: "I drive fast and do not follow traffic rules and I do not meet with an accident."

### Summary of Negations:
1. All continuous functions are not differentiable.
2. Some parents do not care for their children.
3. For all x in R, x^2 ≥ x.
4. There exists n in N such that x^2 + x is not an even number.
5. It is cold or it is raining.
6. n is an even number and 2n is divisible by 4.
7. A triangle is equilateral and it is not equiangular.
8. I drive fast and do not follow traffic rules and I do not meet with an accident.