Solve 5 out of 6 problems.
VI IVII nI-I 'Ivll:
1. Prove or disprove:
(a) For all setsA and B, M U B] = 1A] + |Bl.
(b) Vx e R, ifx < 0 then x3 < 0.
2. Solve the following.
(a) Is the sentence "There are no true sentences" a statement?
I-r'7i'\ 10 l1
Math 221 Discrete Mathematics
Spring 2012 Quiz #1
l 1- Consider the statement: If Mary is not studying, then Mary is _Sleepin9-" NOW: write 53
(a) Converse. (b) inverse. (c) negation. (d) contrapositive.
2. Write the contrapositive of p
p Solve 5 out of 6 problems.
1. Solve the following.
(a) Use mathematical induction to show that, Vn 2 2n2 +1 2 5n.
(b) Find a recursive formula for the sequence_3,621%,24,48,.
/ u A hrl 4, 1+ 4; Q \"\
2 vii Wm. 7 «Li 2 '3 ./ a mum.) WV
1 '53. it Li
, 12 we 3' - i .4":
engtron: is the even or odd .quality of an integer. If two integersare bothoddfor
they are said to have the same parity; if one is odd and one even, they have different parity. V' _;v
' 0 Denition: An integer n