3) Determine either it is True or False int x = 8, y = -3, z = 4; a) (x <= y) && (y > z) b) (x == y) && (z > y) c) (x >= z) || (y <= z) d) (x == z) || (y >= z) e) ! (x != z)
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3) Determine either it is True or False
int x = 8, y = -3, z = 4;
a) (x <= y) && (y > z)
b) (x == y) && (z > y)
c) (x >= z) || (y <= z)
d) (x == z) || (y >= z)
e) ! (x != z)
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- a. Discuss Integer Programming b. Discuss the Application in situations where decision variables must be integers.Problem Description: Implement the described Mancala variant in C++ in the pictures. Player 1 will be a human while the other will be a computer player. The computer player selects a hole following the following decision logic: If there is a hole with enough pieces to finish the turn in the computer player's end zone, select it. Otherwise select the hole on the right to left path with the greatest amount of marbles. If there are no marbles on that path then select the hole closest to the opponent's end zone. It is highly suggested, but not required, to pause the output after the computer makes a move to allow the user to interpret the output before more gets printed out. Look into cin.get(); The program should not allow the player to enter incorrect selections. The player cannot select a nonexistent hole, the end zones, or an empty hole. Look at the example output for an example for how to output the game board formatted in a nice way. You must tell the player what input is valid. For…Translate each of these nested quantifications into an English statement that expresses a mathematicalfact. The domain in each case consists of all real numbers.a) ∃x∀y(x + y = y) b) ∀x∀y (((x ≥ 0) ∧ (y < 0)) → (x − y > 0))c) ∃x∃y(((x ≤ 0) ∧ (y ≤ 0)) ∧ (x − y > 0))d) ∀x∀y((x ≠ 0) ∧ (y ≠ 0) ↔ (xy ≠ 0))
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- Prove the following predicate logic statements valid or invalid: A) ∀x(A(x) → B(x)) ∧ ∀x(A(x) ∨ ¬C(x)) ∧ ∃x(¬B(x)) → ¬∃x(¬A(x) ∧ ¬B(x) ∧ ¬C(x)) B) ∀x(A(x) → B(x)) ∧ ∃x(A(x) ∨ B(x)) → ∃x(A(x) ∧ B(x))Digital Logic Design [1] Simplify the following Boolean functions, using three-variable maps:(a) ?(?, ?, ?) = Σ(0, 2, 6, 7)(b) ?(?, ?, ? )= Σ( 0, 2, 3, 4, 6)(c) ?(?, ?, ? )= Σ( 0, 1, 2, 3, 7)(d) ?(?, ?, ? )= Σ (3, 5, 6, 7)[2] Simplify the following Boolean functions, using four-variable maps:(a) ? (?, ?, ?, ?) = Σ (1, 4, 5, 6, 12, 14, 15)(b) ? (?, ?, ?, ?) = Σ (1, 5, 9, 10, 11, 14, 15)(c) ? (?, ?, ?, ?) = Σ (1, 4, 5, 6, 7, 8, 9)(d) ? (?, ?, ?, ?) = Σ (0, 2, 4, 5, 6, 7, 8, 10, 13, 15)[3] Simplify the following expressions to (1) sum-of-products and (2) products-of sums:(a) ?' ? '+ ?' ?' + ??' + ??(b) ???' + ??' + ??' + ????(c) ? + ? + ? ? + ? + ? ? + ? + ? (? + ? + ?) (d) ???' + ??'? + ???[4] Using K-map derive the minimum SOP expression for each of the followingfunctions: (a) F = ab’c’ + ab’c + abc’ +abc(b) Q = c' + cd + ac + a'bc'd + abc [5] F(w,x,y,z) = Σ (2, 3, 6, 8, 11, 12, 14)(a) Show F on a K-map.(b) Obtain a minimal sum of products expression for F.(c) If the minterms: m4,…Write C# equivalent statements for the following: Consider an example of different types of remotes i.e. AC, TV and Sound System. All of them exhibit some mandatory functionality such as Start (On/Off), Increase volume, Decrease volume, Tune, etc. Explain its implementation with the help of Abstraction, the functionality of a remote.
