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Mathematics in the modern world activty 4

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PROBLEM SOLVING AND REASONING
INDUCTIVE AND DEDUCTIVE REASONING
A. Identify the premise and conclusion in each of the following arguments.
Tell whether also if the following arguments are an inductive or deductive
reasoning.
a) The building of College of Informatics and Computing Sciences in
BatStateU Alangilan is made out of cement. Both building of the College of
Engineering, Architecture and Fine Arts and the College of Industrial
Technology in BatStateU Alangilan are made out of cement. Therefore, all
building of Batangas State University are made out of cement.
Inductive reasoning (specific to general)
First Premise: The building of College of Informatics and Computing
Sciences in BatStateU Alangilan is made out of cement.
Second Premise: Both building of the College of Engineering,
Architecture and Fine Arts and the College of Industrial Technology in
BatStateU Alangilan are made out of cement.
Conclusion: Therefore, all buildings of Batangas State University are
made out of cement.
b) All birds have wings. Eagle is a bird. Therefore, an eagle has wings.
Deductive reasoning (general to specific)
First Premise: All birds have wings.
Second Promise: Eagle is a bird.
Conclusion: Therefore, an eagle has wings.
B. Use inductive reasoning to predict the next three numbers on the
following series of numbers.
a) 3, 7, 11, 15, 19, 23, ____, _____, _____, …
Step 1: Look for a pattern
3 7 11 15 19 23 ?
Step 2: Analyze what is happening in the given pattern
3 7 11 15 19 23
+4 +4 +4 +4 +4
To get the next term, we add 4 to the previous term.
Step 3: Make a conjecture
23 + 4 = 27

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27 + 4 = 31
31 + 4 = 35
Therefore, the next three terms are 27, 31, 35.
b) 1, 2, 6, 15, 31, _____, ______, ______ …
Step 1: Look for a pattern
1 2 6 15 31 … ?
Step 2: Analyze what is happening in the given pattern
1 + 1 = 2 1 + 1
2
= 2
2 + 4 = 6 2 + 2
2
= 6
6 + 9 = 15 6 + 3
2
= 15
15 + 16 = 31 15 + 4
2
= 31
The numbers are added to 1
2
, then 2
2
, then 3
2
, then 4
2
. To get
the next term, we add the previous term with the (n - 1)
2
, wherein n is the
n
th
term
Step 3: Make a conjecture
31 + 25 = 56 31 + 5
2
= 56
56 + 36 = 92 56 + 6
2
= 92
92 + 49 = 141 92 + 7
2
= 141
Therefore, the next three terms are 56, 92, 141.
c) 1, 4, 9, 16, 25, 36, 49, ______, _____, _____, ….
Step 1: Look for a pattern
1 4 9 16 25 36 49 … ?
Step 2: Analyze what is happening in the given pattern
1
2
= 1
2
2
= 4
3
2
= 9
4
2
= 16
5
2
= 25
6
2
= 36
7
2
= 49
The value of the numbers are n
2
, wherein n is the n
th
term. To
get the next term, we use n
2
, wherein n is the
Step 3: Make a conjecture
8
2
= 64
9
2
= 81
10
2
= 100
Therefore, the next three terms are 64, 81, 100
C. Write the next possible equation on the following series of an equation.
37 x 3 = 111
37 x 6 = 222
37 x 9 = 333

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PROBLEM SOLVING AND REASONING INDUCTIVE AND DEDUCTIVE REASONING A. Identify the premise and conclusion in each of the following arguments. Tell whether also if the following arguments are an inductive or deductive reasoning. a) The building of College of Informatics and Computing Sciences in BatStateU Alangilan is made out of cement. Both building of the College of Engineering, Architecture and Fine Arts and the College of Industrial Technology in BatStateU Alangilan are made out of cement. Therefore, all building of Batangas State University are made out of cement. Inductive reasoning (specific to general) First Premise: The building of College of Informatics and Computing Sciences in BatStateU Alangilan is made out of cement. Second Premise: Both building of the College of Engineering, Architecture and Fine Arts and the College of Industrial Technology in BatStateU Alangilan are made out of cement. Conclusion: Therefore, all buildings of Batangas State University are made out of cement. b) All birds have wings. Eagle is a bird. Therefore, an eagle has wings. Deductive reasoning (general to specific) First Premise: All birds have wings. Second Promise: Eagle is a bird. Conclusion: Therefore, an eagle has wings. B. Use inductive reasoning to predict the next three numbers on the following series of numbers. a) 3, 7, 11, 15, 19, 23, ____, _____, _____, … Step 1: Look for a pattern 3 7 11 15 19 23 …? Step 2: Analyze what is happening in the given pattern 3 7 11 15 19 23 ↘ ...
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