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How to draw a network diagram in mathematical foundations of computer science (10mark)
Use the Principle of Mathematical Induction to prove that "((2n) !)\/(2^n n !)" is odd for all positive integers.
Justify whether the given operations on relevant sets are binary operations or not.
- Multiplication and Division on set of natural numbers
- Subtraction and Addition on Set of natural numbers
- Exponential operation: (x, y) → xy on Set of Natural numbers and set of Integers.
Construct a relation on the set {a, b, c, d} that is a. reflexive, symmetric, but not transitive. b. irreflexive, symmetric, and transitive. c. irreflexive, antisymmetric, and not transitive. d. reflexive, neither symmetric nor antisymmetric, and transitive. e. neither reflexive, irreflexive, symmetric, antisymmetric, nor transitive.
Let R1 and R2 be symmetric relations. Is R1 ∩ R2 also symmetric? Is R1 ∪ R2 also symmetric?
(p^q)v(P ^ Q ^ R)
Suppose that A,B and C are sets such that A is the improper subset of B and B is the improper subset of C
Use the truth tables method to determine whether (¬p ∨ q) ∧ (q → ¬r ∧ ¬p) ∧ (p ∧ r) is
satisfiable.
(P^Q^R)V (¬P^Q^R)V(¬P^¬Q^¬R)
Use the Principle of Mathematical Induction to prove that (2𝑛)! /(2n)𝑛! is odd for all positive integers.
