Discrete Math Proofs

Question

# Prove the following statement by induction:

1/(1*2) + 1/(2*3) + ... + 1/(n(n+1)) = n/(n+1), for all integers n>= 1

# Prove by mathematical induction:

5ⁿ + 9 < 6ⁿ for all integers n >= 2.

# Indicate which of the following relationships are true and which are false:

(a) Z+ subset Q
(b) R- subset Q
(c) Q subset Z
(d) Z- U Z+ = Z
(e) Z- intersect Z+ = nullset
(f) Q intersect R = Q
(g) Q U Z = Q
(h) Z+ intersect R = Z+
(i) Z U Q = Z

Use an element argument to prove each statement . Assume that all sets are subset of Universe U.

#For all sets A, B, C, if A subset B then A U C subset B U C.

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