*ਹੇਠ ਲਿਖਿਆਂ ਵਿੱਚੋਂ ਕਿਹੜਾ ਕਥਨ ਸਹੀ ਹੈ ?* 1️⃣ ਦੋ ਪਰਿਮੇਯ ਸੰਖਿਆਵਾਂ ਦਾ ਜੋੜ ਹਮੇਸ਼ਾ ਇੱਕ ਅਪਰਿਮੇਯ ਸੰਖਿਆ ਹੁੰਦੀ ਹੈ। 2️⃣ ਦੋ ਅਪਰਿਮੇਯ ਸੰਖਿਆਵਾਂ ਦਾ ਗੁਣਨਫਲ ਹਮੇਸ਼ਾ ਇੱਕ ਅਪਰਿਮੇਯ ਸੰਖਿਆ ਹੁੰਦਾ ਹੈ। 3️⃣ ਹਰੇਕ ਵਾਸਤਵਿਕ ਸੰਖਿਆ ਇੱਕ ਪਰਿਮੇਯ ਸੰਖਿਆ ਹੈ। 4️⃣ ਹਰੇਕ ਵਾਸਤਵਿਕ ਸੰਖਿਆ ਜਾਂ ਤਾ ਪਰਿਮੇਯ ਹੁੰਦੀ ਹੈ ਜਾਂ ਅਪਰਿਮੇਯ।
Answers
Answer:
Step-by-step explanation:
SOLUTION
TO CHOOSE THE CORRECT OPTION
Which of the following statement is true
1. The sum of two rational numbers is always an irrational number.
2. The product of two irrational numbers is always an irrational number.
3. Every real number is a rational number.
4. Every real number is either rational or irrational.
EVALUATION
CHECKING FOR OPTION : 1
We know that set of rational numbers is closed under addition
Which means if a and b is rational number then a + b is a rational number
Thus the sum of two rational numbers is always an rational number
So this option is not correct
CHECKING FOR OPTION : 2
Take two irrational number as 2 + √3 and 2 - √3
Now ( 2 + √3 ) ( 2 - √3 ) = 4 - 3 = 1
Thus product of two irrational numbers is not always an irrational number
So this option is not correct
CHECKING FOR OPTION : 3
Take a real number ( 2 + √3 )
This is an irrational number not a rational number
So Every real number is not always a rational number
So this option is not correct
CHECKING FOR OPTION : 4
The set of Real numbers can be partitioned into two sets
- Set of rational number
- Set of irrational number
Thus every real number is either rational or irrational
So this option is correct
FINAL ANSWER
Hence the correct option is
4. Every real number is either rational or irrational.
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