Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    1
    ReputationRep:
    Hi guys!

    I'm not sure with some answers for the following 5 sets, it would be amazing if someone could help! I'm mainly getting confused with the bracketing.

    So the Sets are:

    S1= {{B}, B}
    S2={{B}}
    S3={B}
    S4=B={e,f,g}

    And the questions I have...

    1. What is the cardinality of S1?
    I thought it would be 4, as the second B is equivalent to S4 which means it has 4 members. My friend however thinks its 2!

    2. What is the Union of S1 and S2? I thought it might be S1US2= {{B}, B, {{B}}}.

    3.What is the complemet of S1 in S2? S2\S1 = {{B}} or nothing?

    4. What are the subsets of S1? Is it both {A} and A or only {A}? I think it is {A} because this only contains 1 member but I'm unsure!

    5. Which are the subsets of S2? Do I write {{A}} or {A}? I know a set can be a subset of itself but do I leave the outer brackets or keep them on?

    Thanks soo so much in advance! Really feel like I'm struggling a bit and we have a test tomorrow so any help is much appreciated!
    Offline

    22
    ReputationRep:
    [QUOTE=loryn95;68071736]
    So the Sets are:

    S1= {{B}, B}
    S2={{B}}
    S3={B}
    S4=B={e,f,g}

    And the questions I have...

    1. What is the cardinality of S1?
    I thought it would be 4, as the second B is equivalent to S4 which means it has 4 members. My friend however thinks its 2!
    Your friend is right. {B} is an element of S1, it only counts as one element, even if it's a set in its own right, it's still just one element. So there are 2 elements in S1.

    2. What is the Union of S1 and S2? I thought it might be S1US2= {{B}, B, {{B}}}.
    Huh? S1 is the set containing the elements {B} and B. S2 is the set containing the element {B} (it's a subset of S1). So the uniion is the set containing {B} and B and {B}. But note that {B} is the same as {B], to state the obvious. So S1 U S2 = {{B}, B}.

    3.What is the complemet of S1 in S2? S2\S1 = {{B}} or nothing?

    What do you think? What are the elements that are in S2 but not in S1? Is {B} in both S2 and S1? See above...

    4. What are the subsets of S1? Is it both {A} and A or only {A}? I think it is {A} because this only contains 1 member but I'm unsure!
    Where did A come from? There are two elements, so you know that there are 4 subsets. One is the set itself, the other is the empty set. Then the other two are just sets containing single elements.


    5. Which are the subsets of S2? Do I write {{A}} or {A}? I know a set can be a subset of itself but do I leave the outer brackets or keep them on?
    Remember that the empty set is a subset of everything, and you need to keep the inner brackets.

    Thanks soo so much in advance! Really feel like I'm struggling a bit and we have a test tomorrow so any help is much appreciated!
    You really need to get used to the idea of a set being an element in another set, it may help you to write C = {B} and hence S1 = {C, B} or something like that to help cement that idea in your mind.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Would you rather give up salt or pepper?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.