Consider the following in respect of prime number p and composite number c.
1. (p + c)/(p - c) can be even.
2. 2p + c can be odd.
3. pc can be odd.
Which of the statements given above are correct ?
Correct Option: 1, 2 and 3
Let's analyze prime number p and composite number c with respect to the three statements: 1. (p + c)/(p - c) can be even. Let's test values: Let p = 7 (prime) and c = 9 (composite). Then p + c = 16, p - c = -2. 16 / (-2) = -8, which is an even integer! Thus, statement 1 is correct. 2. 2p + c can be odd. Let's test values: Let p = 3 (prime, odd) and c = 9 (composite, odd). Then 2p = 6 (even). 2p + c = 6 + 9 = 15, which is an odd number! Thus, statement 2 is correct. 3. pc can be odd. Let's test values: Let p = 3 (prime, odd) and c = 9 (composite, odd). Then pc = 3 × 9 = 27, which is an odd number! Thus, statement 3 is correct. Since all three statements can be satisfied with valid prime and composite numbers, statements 1, 2, and 3 are all correct.
हिंदी में प्रश्न एवं आदर्श उत्तर
अभाज्य संख्या p और भाज्य संख्या c के बारे में निम्नलिखित पर विचार कीजिए :
1. (p + c)/(p - c) सम हो सकता है ।
2. 2p + c विषम हो सकता है ।
3. pc विषम हो सकता है ।
उपर्युक्त कथनों में से कौन-कौन से सही हैं ?
सही उत्तर: 1, 2 और 3
अभाज्य संख्या p और भाज्य संख्या c के संदर्भ में: 1. यदि p = 7 और c = 9 लें, तो (7 + 9) / (7 - 9) = 16 / (-2) = -8, जो कि एक सम संख्या है (कथन 1 सही है)। 2. यदि p = 3 और c = 9 लें, तो 2p + c = 2(3) + 9 = 15, जो कि एक विषम संख्या है (कथन 2 सही है)। 3. यदि p = 3 और c = 9 लें, तो pc = 3 × 9 = 27, जो कि एक विषम संख्या है (कथन 3 सही है)। अतः तीनों कथन सही हैं।