Propositional Logic Worksheet Page 11
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21More on the Meaning of Implications
Note: In English, a sentence of the form “if A then B” can have
different meanings.
1. Typically there is a causal relationship between A and B, which
is not required in logic.
2. We are often implying more than simply that if A holds, then B
holds as well.
Example:
If I finish my work early, then I will pick you up before lunch.
The common-sense interpretation of this sentence is that the inverse
statement is also true: If I do not finish my work early, then I will
not pick you up before lunch. But this is not implied by the logical
implication P → Q, where P is “I finish my work early” and Q is “I
will pick you up before lunch”. English is not as precise as logic.
Example:
If 2 is prime, then grape juice will pour from the sky today.
Logical implication P → Q can be formed using propositions P and
Q that are not related in any way. We would never say this in English.
11
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education