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"If the BIOS test runs fine, the CPU and motherboard must be OK. If the CPU and the motherboard and memory are all OK, then there must be a flaw in the OS. The BIOS test runs fine and the memory is OK. Therefore there must be a flaw in the OS."
(I) Write the four(4) propositional statement(s) in the above argument.
(II) State the premise(s) and conclusion in the above argument.
(III) Using a truth table, determine the validity or otherwise of this statement.
1+2+3+.....+n = n(n+1)÷2
(I) ~(P ^ ~P)
(II) P implies ~P
(III) (P ^ (p implies q)) implies q
B) show that (P implies Q) implies R is logically equivalent to
(~ P implies R) ^ (Q implies R)
Express each of the following propositions as logical expressions:
(I) If roses are not red, then violets are not blue.
(II) Roses are Red or Violets are not blue.
(III) Either Roses are Red or Violets are Blue (but not both)
∃xP (x) ∧ ∃xQ(x) is true then ∃x(P (x) ∧ Q(x)) is true. ∧
If a function is defined as f(x,n) mod n. Determine the
i. Domain of f
ii. Range of f
iii. G(g(g(g(7)))) if g (n) = f(209, n).
Determine whether the following relations are injective and/or subjective function. Find universe of the functions if they exist.
i. A= v,w,x,y,z, B=1,2,3,4,5
R= (v,z),(w,1), (x,3),(y,5)
ii. A = 1,2,3,4,5 B=1,2,3,4,5
R = (1,2),(2,3),(3,4),(4,5),(5,1)
Determine whether the following relations are injective and/or subjective function. Find universe of the functions if they exist.
i. A= v,w,x,y,z, B=1,2,3,4,5
R= (v,z),(w,1), (x,3),(y,5)
ii. A = 1,2,3,4,5 B=1,2,3,4,5
R = (1,2),(2,3),(3,4),(4,5),(5,1)
If a function is defined as f(x,n) mod n. Determine the
i. Domain of f
ii. Range of f
iii. G(g(g(g(7)))) if g (n) = f(209, n).
#339914 on Dec 2023