1 MTH 125 Venn diagrarn. use regions to determine if ArdBuA\') is eqsivalce so w

Question

1 MTH 125 Venn diagrarn. use regions to determine if ArdBuA') is eqsivalce so whether the following 20. Decide w a. In the science textbook, b. At the health clinic situations represent Deductive or Inductive reasoning. (3 points each represent it is explained that mixing an acid and a base can cause an explosive reaction. a survey was taken to determine how often people washed their hands daily. The c. When a math student added 8 + 2, 10-4 and 16+6 she discovered that the sums are all even mumbers ing soda to create a volcano that patients who washed hands less frequently were more likely to catch colds. because of reasoning (2 points each) 21. a. Write the set ( 5,7,9,11,13,15...) in set builder notation, b. Write a description of the set f 5.7.9,11,13,15... 22. write the roster for this set { x 1 xe N and 298 x 39)- a. b. Write a description of the set { x | xe Nand 298 s 39 } 23. Use inductive reasoning to find the next three terms in the sequence. (3 points each) a. 45,42,39,36, b. 1,1,2,3,5,8,13, 8,13,18,23,27 d. 2,4,8,16,32, -

Explanation / Answer

20)
a) Mixing of acid and base causes an explosion;
Vinegar is acidic and baking soda is basic; So mixing them causes volcano;
This is deductive reasoning since this case has been deduced from a general statement given above about acids and bases;
b) The survey was conducted only for a few people in a clinic about how often they washed their hands;

Then it was concluded that people who washed hands less frequently were more likely to catch cold;
So using the sample of people in the clinic, a generic statement was made;
This is inductive reasonging;

c) 8+2 gave even;
10+4 gave even
16+6 gave even;
Based on this it was said that sums are all evens;
However, only 3 sample set lead to a general statement that sums are all evens;
This is inductive reasoning since a few cases are leading to a generalised answer;

21) a) {5,7,9,11,13,15....} would be { 2x+1 | x>=2 and x is a Natural Number}
b) {5,7,9,11,...} is a set that represents all odd numbers that are greater than or equal to 5;

22 ) a) { x| x belongs to N and 29<= x <= 39} is = {29,30,31,32,33,34,35,36,37,38,39}
b) description of this set would be : A set such that its elements contains all natural numbers between 28 and 40;

23) a) 45,42,39,36 (we see a decrease by 3 units so next 3 numbers would be) = 33,30,27;
b) 1, 1, 2, 3, 5, 8, 13 ... this is a Finonacci series where next term is the sum of two past terms;
= (8+13) , (13+8+13) , ( 8+13 + 13+8+13)
= 21, 34, 55;

In (c) the last term should ideally be 28, in that case next 3 terms would be obtainable by adding 5 to the previous terms; = 33,38,43;

d) 2,4,8,16,32...
each number is obtained by multiplying with 2;
so next 3 numbers will be = 64,128,256;

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