Home
Class 7
MATHS
Which of the following statements are tr...

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

Text Solution

AI Generated Solution

The correct Answer is:
To determine whether the statement \( A \subseteq \{A, B, C\} \) is true, we will analyze the definition of a subset and the elements involved. ### Step-by-Step Solution: 1. **Understanding the Statement**: The statement \( A \subseteq \{A, B, C\} \) means that set \( A \) is a subset of the set containing elements \( A, B, \) and \( C \). 2. **Definition of Subset**: A set \( X \) is a subset of a set \( Y \) (denoted as \( X \subseteq Y \)) if every element of \( X \) is also an element of \( Y \). 3. **Identifying Elements**: In this case, we need to identify what elements are in set \( A \) and in the set \( \{A, B, C\} \). - If we assume \( A \) is an element (not to be confused with the set itself), then the set \( \{A, B, C\} \) contains three elements: \( A, B, \) and \( C \). 4. **Checking the Subset Condition**: For \( A \) to be a subset of \( \{A, B, C\} \), every element of \( A \) must be found in \( \{A, B, C\} \). - If \( A \) is considered as an element, then it is indeed present in the set \( \{A, B, C\} \). 5. **Conclusion**: Since the only element of set \( A \) (assuming it is just the element \( A \)) is present in the set \( \{A, B, C\} \), we can conclude that the statement \( A \subseteq \{A, B, C\} \) is true. ### Final Answer: The statement \( A \subseteq \{A, B, C\} \) is **True**.
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Which of the following statement are true ?

Which of the following statements is/are true ?

Which of the following statements is/are true ?

Which of the following statement is /are true ?

Which of the following statements is/are true ?

Which of the following statements is/are true ?

Which of the following statements is/are true ?

Which of the following statements is/are true?

Which of the following statements is/are true?

Which of the following statements is true?

ICSE-SETS -EXERCISE 6 B
  1. How many subsets in all are there of a set containing 4 elements ?

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |