Which of the following statements is/are False? S₁ : , n N , such that n^2 + n + 2 is divisible by 4. S₂ : , x N , such that x - 17 S₃ : , n N, x^2 + 3x - 10 = 0 . S₄ : , n N, n^2 1 .

Step-by-step solution

For S₁ : Let n = 1 N . Then n^2 + n + 2 = 1^2 + 1 + 2 = 4 , which is divisible by 4 . Thus, there exists at least one natural number satisfying the condition, making S₁ true. For S₂ : Let x = 1 N . Then x - 17 = 1 - 17 = -16 , which is strictly less than 20 . Thus, there exists at least one natural number satisfying the condition, making S₂ true. For S₃ : The statement asserts that for all natural numbers, the equation x^2 + 3x - 10 = 0 holds. However, x^2 + 3x - 10 = (x + 5)(x - 2) = 0 is only satisfied for x = 2