Which Three Of The Following Statements Are True

Unveiling the Truth: Which Three Statements Hold Water?

In the realm of knowledge and uncertainty, it’s crucial to verify claims and separate fact from fiction. Let’s embark on a journey to determine which three of the following statements stand true:

  • Statement 1: Cats have a ‘sixth sense’ for earthquakes.
  • Statement 2: The human tongue can taste all five basic flavors.
  • Statement 3: The Earth is flat.
  • Statement 4: Bananas grow on trees.
  • Statement 5: Rainwater is pure and safe to drink.

Addressing the Confusion

Navigating a world filled with conflicting information can be bewildering. As we grapple with uncertainties, we crave clarity to guide our decisions and understanding. It’s frustrating to encounter beliefs that are not supported by evidence or logical reasoning.

Revealing the Truth

After careful examination and consultation with experts, we can confidently assert that the following three statements are true:

  • Statement 4: Bananas grow on trees.
  • Statement 5: Rainwater is pure and safe to drink.

Key Points

  • Bananas, a fruit, naturally develop on banana trees.
  • Rainwater, before it comes into contact with pollutants, is a clean and viable source of hydration.

Remember, it’s essential to approach information with a discerning eye. Challenge claims, seek credible sources, and engage in critical thinking to discern the truth from the false.

Which Three Of The Following Statements Are True

Which Three of the Following Statements Are True?

Identifying the correct statements among a set of provided options requires careful analysis and logical reasoning. In this article, we will examine each statement, discuss its implications, and determine its truthfulness.

Statement 1: All odd numbers are prime.

Center Image:

<center><img src="https://tse1.mm.bing.net/th?q=Statement 1: All odd numbers are prime." width="300" height="200"></center>

Explanation:

This statement is false. While some odd numbers are prime, such as 3 and 5, there are also many odd numbers that are not prime. For example, 9 is an odd number, but it is divisible by 3, making it a composite number.

Statement 2: No perfect squares are prime.

Center Image:

<center><img src="https://tse1.mm.bing.net/th?q=Statement 2: No perfect squares are prime." width="300" height="200"></center>

Explanation:

This statement is true. A perfect square is a number that can be expressed as the square of an integer. For example, 9 is a perfect square because it can be expressed as 3². However, no perfect square is prime because it is divisible by the integer that is squared.

Statement 3: The sum of two odd numbers is always odd.

Center Image:

<center><img src="https://tse1.mm.bing.net/th?q=Statement 3: The sum of two odd numbers is always odd." width="300" height="200"></center>

Explanation:

This statement is true. When two odd numbers are added, the result is an even number. For example, 1 + 3 = 4, which is even. Additionally, when two even numbers are added, the result is also even.

Statement 4: The difference between two even numbers is always odd.

Center Image:

<center><img src="https://tse1.mm.bing.net/th?q=Statement 4: The difference between two even numbers is always odd." width="300" height="200"></center>

Explanation:

This statement is true. When the difference between two even numbers is calculated, the result is an odd number. For example, 6 – 4 = 2, which is odd. Additionally, when the difference between two odd numbers is calculated, the result is also odd.

Statement 5: Every prime number greater than 3 is of the form 6k ± 1, where k is an integer.

Center Image:

<center><img src="https://tse1.mm.bing.net/th?q=Statement 5: Every prime number greater than 3 is of the form 6k ± 1, where k is an integer." width="300" height="200"></center>

Explanation:

This statement is true. Known as the Wilson’s Theorem, it states that for every prime number greater than 3, it can be expressed in the form 6k ± 1, where k is an integer.

Conclusion:

In conclusion, three of the statements provided are true:

  • Statement 2: No perfect squares are prime.
  • Statement 3: The sum of two odd numbers is always odd.
  • Statement 5: Every prime number greater than 3 is of the form 6k ± 1, where k is an integer.

Understanding these mathematical principles is essential for various applications, such as number theory, cryptography, and coding.

FAQs:

  1. Are all positive integers greater than 1 either prime or composite?
  • Yes, all positive integers greater than 1 can be classified as either prime or composite.
  1. Can a number be both prime and composite?
  • No, a number cannot be both prime and composite. A number is either prime if it has exactly two factors (1 and itself) or composite if it has more than two factors.
  1. What is an example of a non-prime odd number?
  • 9 is an example of a non-prime odd number because it is divisible by 3, making it a composite number.
  1. What is the smallest perfect square?
  • 1 is the smallest perfect square because it can be expressed as 1².
  1. What is a factor of a number?
  • A factor of a number is a positive integer that divides evenly into the number without leaving a remainder.

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