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Which of the following statements are tr...

Which of the following statements are true ?
`phi sub {a,b,c} `

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To determine whether the statement "φ is a subset of {a, b, c}" is true, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Terminology**: - The symbol "φ" represents the null set or empty set, which contains no elements. - A subset is a set where every element of the subset is also an element of the larger set. 2. **Identify the Larger Set**: - In this case, the larger set is {a, b, c}. This set contains three elements: a, b, and c. 3. **Evaluate the Null Set**: - The null set φ has no elements. Therefore, there are no elements in φ that could possibly not be in {a, b, c}. 4. **Check the Definition of Subset**: - For φ to be a subset of {a, b, c}, every element of φ (which is none) must be in {a, b, c}. Since there are no elements in φ, this condition is trivially satisfied. 5. **Conclusion**: - Since the null set is a subset of every set, we can conclude that the statement "φ is a subset of {a, b, c}" is true. ### Final Answer: The statement "φ is a subset of {a, b, c}" is true. ---
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ICSE-SETS -EXERCISE 6 B
  1. How many subsets in all are there of a set containing 4 elements ?

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  2. How many subsets in all are there of a set with cardinal number 6?

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  3. How many proper subsets in all are there of a set containing 3 element...

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  4. How many proper subsets in all are there of a set with cardrinal numbe...

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  5. Which of the following statements are true ? { a} sub {a,b,c,}

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  6. Which of the following statements are true ? {a} sub {b,c,d,e}

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  7. Which of the following statements are true ? phi sub {a,b,c}

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  8. Which of the following statements are true ? phi in {a,b,c}

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  9. Which of the following statements are true ? 0 cancel in phi

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  10. Which of the following statements are true ? {1} sub {0,1}

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  11. Which of the following statements are true ? Every subset of a fin...

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  12. Which of the following statements are true ? Every subset of an infi...

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  13. Let A = { 1,2,3,4,5,6,7,8,9 , 10 ,1 1 , 12, } Write the subset of ...

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  14. Let A = { 1,2,3,4,5,6,7,8,9 , 10 ,1 1 , 12, } Write the subset of ...

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  15. Let A = { 1,2,3,4,5,6,7,8,9 , 10 ,1 1 , 12, } Write the subset of ...

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  16. Let U= { 5,6,7,8,9 , 10 , 11 , 12 ,13 ,14 , 15 , 16} be the universal...

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  17. Let the set I of all integers be the universal set and let A ={x: x ...

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  18. Suggest a universal set for the sets given below : (5,7,9) , (3,5,...

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  19. Suggest a universal set for the sets given below : [ odd number...

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  20. Suggest a universal set for the sets given below : [vowels in Engli...

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