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Let D be the set of tuples ( w1,w2,. .,w10), where wi £{1,2,3}, 1≤i≤10 and wi wi 1 is an even number for each i with 1≤i≤9. Then the number of elements in D is 1. 2^11 1. 2. 2^10 1. 3. 3^10 1. 4. 3^11 1?
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Let D be the set of tuples ( w1,w2,. .,w10), where wi £{1,2,3}, 1≤i≤10...
Given:
- Set D consists of tuples (w1,w2,...,w10), where wi € {1,2,3}, 1 ≤ i ≤ 10.
- wi wi 1 is an even number for each i with 1 ≤ i ≤ 9.
To Find:
Number of elements in D.
Solution:
Step 1: Finding the possible values of w1,w2,...,w10.
- Since wi € {1,2,3}, there are 3 possible values for each wi.
- For w1, since wi wi 1 is even, it can only take the values 2 or 3.
- For w2 to w9, since wi wi 1 is even, they can only take the values 1 or 3.
- For w10, there are no constraints, so it can take any value from {1,2,3}.
Step 2: Finding the number of elements in D.
- The number of possible values for w1 is 2 (2 or 3).
- The number of possible values for w2 to w9 is 2 (1 or 3).
- The number of possible values for w10 is 3 (1, 2, or 3).
Step 3: Applying the multiplication principle.
- The number of elements in D can be found by multiplying the number of possible values for each wi.
- Number of elements in D = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 = 2^9 * 3 = 2^(9+1) * 3^1 = 2^10 * 3^1
Answer:
- The number of elements in D is 2^10 * 3^1.
- Set D consists of tuples (w1,w2,...,w10), where wi € {1,2,3}, 1 ≤ i ≤ 10.
- wi wi 1 is an even number for each i with 1 ≤ i ≤ 9.
To Find:
Number of elements in D.
Solution:
Step 1: Finding the possible values of w1,w2,...,w10.
- Since wi € {1,2,3}, there are 3 possible values for each wi.
- For w1, since wi wi 1 is even, it can only take the values 2 or 3.
- For w2 to w9, since wi wi 1 is even, they can only take the values 1 or 3.
- For w10, there are no constraints, so it can take any value from {1,2,3}.
Step 2: Finding the number of elements in D.
- The number of possible values for w1 is 2 (2 or 3).
- The number of possible values for w2 to w9 is 2 (1 or 3).
- The number of possible values for w10 is 3 (1, 2, or 3).
Step 3: Applying the multiplication principle.
- The number of elements in D can be found by multiplying the number of possible values for each wi.
- Number of elements in D = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 = 2^9 * 3 = 2^(9+1) * 3^1 = 2^10 * 3^1
Answer:
- The number of elements in D is 2^10 * 3^1.
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Let D be the set of tuples ( w1,w2,. .,w10), where wi £{1,2,3}, 1≤i≤10 and wi wi 1 is an even number for each i with 1≤i≤9. Then the number of elements in D is 1. 2^11 1. 2. 2^10 1. 3. 3^10 1. 4. 3^11 1?
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Let D be the set of tuples ( w1,w2,. .,w10), where wi £{1,2,3}, 1≤i≤10 and wi wi 1 is an even number for each i with 1≤i≤9. Then the number of elements in D is 1. 2^11 1. 2. 2^10 1. 3. 3^10 1. 4. 3^11 1? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let D be the set of tuples ( w1,w2,. .,w10), where wi £{1,2,3}, 1≤i≤10 and wi wi 1 is an even number for each i with 1≤i≤9. Then the number of elements in D is 1. 2^11 1. 2. 2^10 1. 3. 3^10 1. 4. 3^11 1? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let D be the set of tuples ( w1,w2,. .,w10), where wi £{1,2,3}, 1≤i≤10 and wi wi 1 is an even number for each i with 1≤i≤9. Then the number of elements in D is 1. 2^11 1. 2. 2^10 1. 3. 3^10 1. 4. 3^11 1?.
Let D be the set of tuples ( w1,w2,. .,w10), where wi £{1,2,3}, 1≤i≤10 and wi wi 1 is an even number for each i with 1≤i≤9. Then the number of elements in D is 1. 2^11 1. 2. 2^10 1. 3. 3^10 1. 4. 3^11 1? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let D be the set of tuples ( w1,w2,. .,w10), where wi £{1,2,3}, 1≤i≤10 and wi wi 1 is an even number for each i with 1≤i≤9. Then the number of elements in D is 1. 2^11 1. 2. 2^10 1. 3. 3^10 1. 4. 3^11 1? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let D be the set of tuples ( w1,w2,. .,w10), where wi £{1,2,3}, 1≤i≤10 and wi wi 1 is an even number for each i with 1≤i≤9. Then the number of elements in D is 1. 2^11 1. 2. 2^10 1. 3. 3^10 1. 4. 3^11 1?.
Solutions for Let D be the set of tuples ( w1,w2,. .,w10), where wi £{1,2,3}, 1≤i≤10 and wi wi 1 is an even number for each i with 1≤i≤9. Then the number of elements in D is 1. 2^11 1. 2. 2^10 1. 3. 3^10 1. 4. 3^11 1? in English & in Hindi are available as part of our courses for Mathematics.
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