1. a)Suppose that fis defined recursively by:f (0) = 5 and f(n+1) = 2 fn+5. Find A(1), A2), (3) and {(4)?b)For which positive integer n is it true that 2" > n³?c)Prove your answer in (b) above using mathematical induction.d)Give a recursive definition of the sequence {an}, n= 1, 2, 3...ifan = 2" + 1e)Use your definition in (d) above to finda10,and a15f)Let A = {1, 2, {{1,2}}}. Find the power set P(A) 2. а)Define the following with an example:i)Contradictionii)Propositionb)Show that (p → q)^(p →r)is a Contingency.c)Use quantifiers to express the statement “if somebody isfemale and is a parent, then this person is someone's motherd)Let p and q be the propositions:p: I will doevery exercise in this bookq: I will get an 'A’ in this courseWrite the following propositions using p and q and logicalconnectives.i)For me to get an 'A’ in this course it is necessary andsufficient that I do every exercise in this book.ii)Construct the truth table for your proposition in d(i) above.e)i)Write down the output Boolean expression using p, q and rfor the circuit gates below:ii)if p = 1, q = 0 and r= 1 find the output signal for thecircuit below:pr

Name: 1. a)Suppose that fis defined recursively by:f (0) = 5 and f(n+1) = 2
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Description: 1. a)Suppose that fis defined recursively by:f (0) = 5 and f(n+1) = 2 fn+5. Find A(1), A2), (3) and {(4)?b)For which positive integer n is it true that 2" > n³?c)Prove your answer in (b) above using mathematical induction.d)Give a recursive definiti

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a) Suppose that fis defined recursively by: f(0) = 5 and f(n+1) = 2 fn +5. Find f{(1), {2), A3) and f(4)? b) For which positive integer n is it true that 2" > n³? c) Prove your answer in (b) above using mathematical induction.

a) Suppose that fis defined recursively by: f(0) = 5 and f(n+1) = 2 fn +5. Find f{(1), {2), A3) and f(4)? b) For which positive integer n is it true that 2" > n³? c) Prove your answer in (b) above using mathematical induction.

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Chapter2: Second-order Linear Odes

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Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Topic Video

Question

1. a)
Suppose that fis defined recursively by:
f (0) = 5 and f(n+1) = 2 fn+5. Find A(1), A2), (3) and {(4)?
b)
For which positive integer n is it true that 2" > n³?
c)
Prove your answer in (b) above using mathematical induction.
d)
Give a recursive definition of the sequence {an}, n= 1, 2, 3...
if
an = 2" + 1
e)
Use your definition in (d) above to find
a10,
and a15
f)
Let A = {1, 2, {{1,2}}}. Find the power set P(A)

2. а)
Define the following with an example:
i)
Contradiction
ii)
Proposition
b)
Show that (p → q)^(p →r)is a Contingency.
c)
Use quantifiers to express the statement “if somebody is
female and is a parent, then this person is someone's mother
d)
Let p and q be the propositions:
p: I will do
every exercise in this book
q: I will get an 'A’ in this course
Write the following propositions using p and q and logical
connectives.
i)
For me to get an 'A’ in this course it is necessary and
sufficient that I do every exercise in this book.
ii)
Construct the truth table for your proposition in d(i) above.
e)
i)
Write down the output Boolean expression using p, q and r
for the circuit gates below:
ii)
if p = 1, q = 0 and r= 1 find the output signal for the
circuit below:
p
r

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