Question

Match the following. Given D = {x | x is a whole number} E = {x | x is a perfect square < 100} F = {x | x is an even number between 10 and 20} 1. D ∩ (E ∪ F) {1, 4, 9, 16, 25, 36, 49, 64, 81, 12, 14, 18} 2. D ∩ E {1, 4, 9, 16, 25, 36, 49, 64, 81} 3. D ∪ (E ∩ F) {12, 14, 16, 18} 4. D ∩ (E ∩ F) {all whole numbers} 5. D ∩ F {16}

Answer 1

The values of the set functions after the matching are:

• D∩F = F
• D∩E = E
• DU(E∩F) = D
• D∩(E∩F) = {16}
• D∩(EUF) = {1,,4,9,12.14,16,18,35,36,47,64,81}

What do we mean by different types of sets' functions?

• The intersection of two sets is represented by ∩.
• This refers to shared values between the sets under consideration.
• U represents the union of two sets.
• This includes all values from all sets considered.

So, we have D = {x | x is a whole number}.

• Then: D = {0,1,2,3,4,5,6,7,8,.........}

Similiarly, E = {x | x is a perfect square < 100}.

• So: E = {1,,4,9,16,35,36,47,64,81}

Similarly, F = {x | x is an even number between 10 and 20}.

• Then: F = {12,14,16,18}

Now, D∩E = The common values from sets D and E.

• Here we have: = E (all perfect square < 100 )

D∩F = F

• Where: This means all even numbers between 10 and 20}

Now, D∩(E∩F) = {16}.

• Then: E∩F = {16}
• Hence,  The only value common to both set D and E∩F is 16.

DU(E∩F) = D ( This means all whole numbers)

• Then we can say: E∩F = {16}

D∩(EUF) = {1,,4,9,12.14,16,18,35,36,47,64,81}

• We obtain: EUF = {1,,4,9,12.14,16,18,35,36,47,64,81}

Therefore, the values after the matching are:

• D∩F = F
• D∩E = E
• DU(E∩F) = D
• D∩(E∩F) = {16}
• D∩(EUF) = {1,,4,9,12.14,16,18,35,36,47,64,81}

Know more about sets functions here:

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