If the statement "If the sun is shining, then it's not raining" is assumed to be true, is its reverse, "If it's not raining, then the sun must be shining," also always true?
2007-01-23 02:54:54 · 13 answers · asked by Rattiesrule 2 in Science & Mathematics ➔ Other - Science
No, that could be happen that it's not raining while the sun may not shin, the sun could be hiding behind the cloud, that is my counterexample.
2007-01-23 02:57:51 · answer #1 · answered by Anonymous · 1⤊ 0⤋
Let
A = The sun is shining
B = It's not raining.
The the statement "If the sun is shining, then it's not raining" translates in mathematical terms to :
If A then B or A => B
However if A => B is true then B => A may or may not be true. We have too little information.
So we cannot always say that "If it's not raining, then the sun must be shining,"
2007-01-23 11:01:29 · answer #2 · answered by Manisha 4 · 0⤊ 0⤋
Neither statement is true, empirically. And even if you assume the first statement is true, the second need not be true. You would have to assume that it is either raining or the sun is shining (excluded middle), which is fine in a narrowly-defined logic system, but not in the real world. You would never have a rainbow if both statements were true.
2007-01-23 11:38:15 · answer #3 · answered by thylawyer 7 · 0⤊ 0⤋
The sun is always shining on one side of the earth despite the weather. However it may not be raining but the sun may also not be shining on the ground if there are clouds. Also if the sun is shining, then it's not raining is not always true. Rainbows appear when it is raining in the distance but sunny where you are standing.
2007-01-23 11:01:20 · answer #4 · answered by Kes 7 · 0⤊ 0⤋
The saying is short hand for
If the sun is shining there are no clouds,
there must be clouds for it to rain,
therefore it's not raining.
The reverse is something like,
If the sun is not shining, it might be night or it might be cloudy,
if it is night, it does not have to be raining
if it is cloudy, it might not be raining (it might be snowing, or just overcast.)
therefore the statement, "if it's not raining, then the sun must be shining" is not always true. "If it's not raining, then the sun might be shining" is true.
2007-01-23 11:03:39 · answer #5 · answered by Mike1942f 7 · 0⤊ 0⤋
No. By classical dedustive reasoning, if "P then Q" is assumed to be true and P is true, the Q is said to be true too. But if only Q is true, we cannot conclude that P is true. It would be a form of illogical reasoning. In other words, if it's not raining, we cannot conclude that the sun is shining.
2007-01-23 11:03:53 · answer #6 · answered by vv 1 · 0⤊ 0⤋
NO! If it's raining then the sun is not shining . would be the reverse!
2007-01-23 10:58:45 · answer #7 · answered by roseysuzy1128 2 · 1⤊ 0⤋
It would not be true as there could be other possibilities. For example, it could not be raining and it could be night time. It could not be raining, but it could be snowing....etc.
2007-01-23 10:58:48 · answer #8 · answered by Kerry 7 · 2⤊ 0⤋
No that is not always true.
For I have seen it rain on a clear day .
and it also rains at night.
2007-01-23 10:58:38 · answer #9 · answered by Anonymous · 1⤊ 0⤋
I love "sun showers"
2007-01-23 11:23:38 · answer #10 · answered by higg1966 5 · 0⤊ 0⤋