Which of the following statements is true ?
Correct Answer :
Mathematical statements can be conditional.
Solution :
The correct option is Mathematical statements can be conditional.
Let us analyze each of the given options step-by-step to understand why this statement is true and why the others are incorrect:
1. "Mathematical statements can be conditional."
This is a fundamental property of logic and mathematics. A conditional statement has the form "If P, then Q" (often written as ), where P is the hypothesis and Q is the conclusion. Many mathematical definitions, theorems, and implications are structured conditionally (for example, "If a triangle is equilateral, then it is isosceles"). Therefore, this statement is true.
2. "Mathematics consists of all the theorems proved in mathematics books."
Mathematics is a dynamic, expanding discipline. It is not limited to already recorded or published theorems; it encompasses problem-solving, pattern recognition, logical reasoning, and newly discovered concepts. Thus, defining mathematics strictly as a collection of existing proved theorems is overly restrictive and false.
3. "A person good in arithmetical computation is also good in Mathematics and vice-versa."
Arithmetic operations (addition, multiplication, etc.) are only a small branch of mathematics. Higher mathematics relies heavily on abstract thinking, logic, spatial reasoning, and creativity. Being quick at calculations does not guarantee strength in mathematical logic or proof-based mathematics, nor does being a good mathematician require being a fast mental computer. Thus, this statement is false.
4. "Intuition has no role in generating mathematical knowledge."
Intuition, visualization, and creative guessing play a vital role in formulating conjectures and developing new mathematical insights. Formal logic and proof are used to verify ideas, but intuition often serves as the initial spark for discovery. Hence, this statement is false.
Therefore, the only true statement among the options is that mathematical statements can be conditional.
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