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x'y'+xz'+yz+x'yz'+xy'z
Can you help me simplify this expression? Thank you! Please explain how you did it.
Let f:Bᴣ →B with S(f) ={(0,0,0),(0,0,1),(1,0,0),(1,1,0)}.Find a simplest Boolean expression that represents the function f(x,y,z).
Establish the equivalence: (P→Q)→(P Λ Q) ≡ (~P+Q)Λ (Q→P)
3 questions in discrete mathematics.

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Six students : Ash , Betty , Cheryl , Diana ,Emeline and Fiona are required to form a line ( one behind the other ) for an inspection. In how many ways can this be done if Diana must be between Fiona and Cheryl ? Explain your answer.
Let S ={100, 101, 102,....999} so that |S| = 900.
a) How many numbers in S have at least one digit that is a 3 or 7? Examples... 300, 707, 103.
b) How many numbers in S have at least one digit that is a 3 and a 7? Examples.... 736 and 377
For any statements p, q, prove that
a) ¬(p ↓ q)⇐⇒(¬p ↑¬q)
b) ¬(p ↑ q)⇐⇒(¬p ↓¬q)
Problem 4
Determine |A ∪ B ∪ C| when |A|= 50, |B|= 500, and
|C| 5000, if (a)A ⊆ B ⊆ C; (b)A ∩ B A ∩ C B ∩ C
∅; and (c) |A ∩ B| |A ∩ C| |B ∩ C| 3 and |A ∩ B ∩ C| 1.
If set S has n elements how many subsets have an even # of elements?
i have a question and i think that you can help me,so there is a person in courts and the judge says to the person if u speak the truth we will backed you and eat you and if you lie we will simmer and eat you,so what must to do or to say the persont to save himself?
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