Question 1
(a)
In each case, say whether the indicated function is one-to-one and onto.
if : R+ → R+ defined by f(x) = 2x
iig : R+ → N defined by g(x) = ⌊x⌋ ( the largest integer ≤ x)
3 Marks
(b)
Derive the string a + (a * a) / a – a using leftmost derivation and rightmost derivation forfollowing grammar.G : S → S + S | S – S | S * S | S/S | ( S ) | a4 Marks
(c)
iUsing the principle of Mathematical Induction, Prove that for every n ≥ 1, ii. In following case, a relation on the set {1, 2, 3} is given. Of the three properties, reflexivity, symmetry, and transitivity, determine which ones the relation has. Give reasons. R ={ (1, 1), (2, 2), (3, 3), (1, 2) }
i)Using the principle of Mathematical Induction, Prove that for
every n ≥ 1, ii. In following case, a relation on the set {1, 2, 3} is given. Of
the three properties, reflexivity, symmetry, and transitivity,
determine which ones the relation has. Give reasons.
R ={ (1,
1), (2,
2), (3,
3), (1,
2)}
7 Marks
