A logical argument consists of one or more premises followed by one or more conclusions. The conclusion of a logical argument may be valid or invalid.
A premise is a statement that helps support a conclusion. Examples of premises are:
A conclusion is a statement that may follow from the premises. If the logic in the argument is used correctly, the conclusion is valid. If the logic in the argument is not used correctly, the conclusion is invalid. Examples of conclusions are:
There are five types of logical arguments that, if used correctly, will have a valid conclusion. If these types of logical arguments are used incorrectly, any conclusions will be invalid.
Name | Definition | Example |
---|---|---|
Direct Argument | If p is true then q is true. | If a shape is a square, then it is a rectangle. |
p is true. | HIJK is a square. | |
Therefore q must also be true. | Therefore HIJK must also be a rectangle. | |
Indirect Argument | If p is true then q is true. | If a shape is a square, then it is a rectangle. |
q is not true. | HIJK is not a rectangle. | |
Therefore p can not be true. | Therefore HIJK can not be a square. | |
Chain Rule | if p is true, then q is true. | If a shape is a square, then it is a rectangle. |
if q is true, then r is true. | If a shape is a rectangle, then it is a parallelogram. | |
Therefore, if p is true, then r is true. | Therefore, if a shape is a square, then it is a parallelogram. | |
Or Rule | Either p is true or q is true. | Figure A is a circle or a square. |
p is not true. | Figure A is not a circle. | |
So q must be true. | So figure A must be a square. | |
And Rule | p and q are not both true. | Figure A is not both a circle and a square. |
q is true. | Figure A is a square. | |
So p must be false. | So figure A can not be a circle. | |
Table 1: Five types of logical arguments |
Examine each logical argument. Identify the type of logical argument in the list in table 1. Click on Type of logical argument to see if your answer is correct. Then decide if the conclusion is valid or invalid. Click on Valid or invalid to see if your answer is correct.
Logical argument | Type of logical argument | Is argument valid or invalid |
---|---|---|
if y = 3 then
y^{2} - 4 = 5. y^{2} - 4 ≠ 5. Therefore y ≠ 3. | Type of logical argumentIndirect argument | Valid or invalid Valid |
Child A is either
a boy or a girl. Child A is not a boy. Therefore child A is not a girl. | Type of logical argumentOr rule | Valid or invalid Invalid. The consistent conclusion is that child A must be a girl. |
Table 2: Understanding check |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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