I need help with these two question. Can you please help me help me. Prove or Di
ID: 3198144 • Letter: I
Question
I need help with these two question. Can you please help me help me.
Prove or Disprove (make sure to show and clearly identify all steps and give justifications for each step): For all integers x and y, if x is even and y is even, then xty is even. Use Set B defined below to answer parts a-d B-(Desire), (Emma, Farooq), Emma, Farooq, (Desire, Emma, Farooq)) a. What is the cardinality of Set B? b. True or False? Desire, Emma, Farooq) E B C. True or False? [Desire)S B d. Create a valid subset with at least 2 elements of Set B.Explanation / Answer
1. If x is even and y is even,
Let x = 2k and y = 2l where k and l are integers.
Adding => x + y = 2k + 2l = 2 (k + l)
Since RHS has a factor 2, LHS must be divisible by 2.
=> 2 | x + y => x + y is even.
2. B = {{Desire}, {Emma, Farooq}, Emma, Farooq, {Desire, Emma, Farooq}}.
a. Since B has five elements, cardinality of set B is 5.
b. The last element is {Desire, Emma, Farooq}.
Therefore, the statement is true.
c. {Desire} is the first element of B. However, there is no element Desire and hence no subset {Desire}.
Therefore, the statement is false.
d. One valid subset is
{{Desire}, Emma, Farooq}.