Not register? Register Now!
Essay Available:
You are here:
Pages:
11 pages/≈6050 words
Sources:
No Sources
Level:
Other
Subject:
Psychology
Type:
Coursework
Language:
English (U.S.)
Document:
MS Word
Date:
Total cost:
\$ 39.95
Topic:

# Introduction to Logic: Mathematical Literacy (Coursework Sample)

Instructions:

Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system.

source..
Content:

Introduction to Logic (Mathematical Literacy)
1 Hypothesis and conclusion
LOGIC, we could say, is the study of If − then sentences.
If a number is divisible by 10, then it is divisible by 2.
The clause introduced by If –
A number is divisible by 10
– is called the hypothesis.
It is what we are given, or what we may assume. The clause introduced by then –
It is divisible by 2
–is called the conclusion.
☞ Conclusion is the statement that “follows” from the hypothesis. Or, given the hypoth- esis, it is the statement that we must prove.
2 Necessary and sufficient conditions
Sufficient Condition: When the If −then sentence is true, we say that the hypothesis is a sufficient condition for the conclusion.
Thus it is sufficient to know that a number is divisible by 10 – in order to conclude that it is divisible by 2.
Necessary Condition: The conclusion is then called a necessary condition of that hypothesis.
Because it necessarily follows that the number will be divisible by 2, if it is divisible by 10.
Remark. The hypothesis is a sentence, independent of “If”, and the conclusion is a sentence, independent of “then.”
Problem 1. If two numbers are even, then their sum is even.
1 Name the hypothesis and the conclusion.
2 Which of them is the sufficient condition, and which the necessary condition?
Answer.(i). Hypothesis: Two numbers are even.
Conclusion: Their sum is even.
(ii). Since the statement is true, we have, Sufficient Condition: Two numbers are even. Necessary Condition: Their sum is even.
Problem 2. A number is divisible by 3 if it is divisible by 6.
Name the hypothesis and the conclusion. Which of them is the sufficient condition, and which the necessary condition?
Answer. The hypothesis is “A number is divisible by 6.” It is that clause which follows “if.” It is the sufficient condition, because the statement is true.
The conclusion is “The number is divisible by 3.” It is the necessary condition.
Problem 3. If a number ends in 0, then it is a multiple of 5.
* Name the hypothesis and the conclusion.
* Is the hypothesis a sufficient condition for that conclusion?
Answer.(i). Hypothesis: A number ends in 0.
Conclusion: It is a multiple of 5.
(ii). Yes, because the statement is true.
Problem 4. If a number is a multiple of 5, then it ends in 0.
* Name the hypothesis and the conclusion.
* Is the hypothesis a sufficient condition for that conclusion?
Answer.(i). Hypothesis: A number is a multiple of 5.
Conclusion: It ends in 0.
(ii). No, because the statement is false. 15 is a multiple of 5, but 15 does not end in 0.

...
Get the Whole Paper!
Not exactly what you need?
Do you need a custom essay? Order right now:

### Other Topics:

• Lawrence Kohlberg's Theory of Moral Development
Description: Lawrence Kohlberg (1958) agreed with Piaget’s 1932 theory of moral development in principle but wanted to develop his ideas further. He used Piaget storytelling method to tell people stories involving moral dilemmas, in each case, he presented a choice to be considered, for example between the rights of...
4 pages/≈1100 words| 1 Source | Other | Psychology | Coursework |
• Physiology of hearing 304 Psychology Coursework Essay
Description: The ear is a very important organ in the body of human beings. It performs two main functions, balancing and hearing. The ear has got three main parts, the outer or the external ear, the middle ear, and the inner ear. The external ear is made up of the pinna which is the outermost part...
1 page/≈275 words| 3 Sources | Other | Psychology | Coursework |
Need a Custom Essay Written?
First time 15% Discount!