The truth value of a conditional statement is not dependent on the truth values of its constituents, only how they relate to one another. 6 times out of 7, it is not Monday, but regardless of weather "today is Monday" is true, it follows that when it is Monday, it will be Tuesday. On Saturdays, the statement "tomorrow is Sunday" is true, but it as a conclusion does not follow from the condition "today is Monday", so the overall statement is false. In the third statement, there is no causal connection between dogs having 3 heads, and dogs flying; the conclusion does not follow from the premise, therefore it is false. It's just as easy to imagine a hypothetical where dogs have 3 heads and fly as one where dogs have 3 heads and don't. In the fourth statement, the conclusion is something that is true in all conditions, regardless of their truth values, and thus it is overall true. Even if hypothetically, sharks walked on land, 1+1 would still be 2.
What about for multiple conclusions? For example, "If the sky is green, then birds can swim and cats can fly." So, as long as the first hypothesis is false, the truth value of a conditional will always be true?
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The truth value of a conditional statement is not dependent on the truth values of its constituents, only how they relate to one another. 6 times out of 7, it is not Monday, but regardless of weather "today is Monday" is true, it follows that when it is Monday, it will be Tuesday. On Saturdays, the statement "tomorrow is Sunday" is true, but it as a conclusion does not follow from the condition "today is Monday", so the overall statement is false. In the third statement, there is no causal connection between dogs having 3 heads, and dogs flying; the conclusion does not follow from the premise, therefore it is false. It's just as easy to imagine a hypothetical where dogs have 3 heads and fly as one where dogs have 3 heads and don't. In the fourth statement, the conclusion is something that is true in all conditions, regardless of their truth values, and thus it is overall true. Even if hypothetically, sharks walked on land, 1+1 would still be 2.
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What about for multiple conclusions? For example, "If the sky is green, then birds can swim and cats can fly." So, as long as the first hypothesis is false, the truth value of a conditional will always be true?
Yeah buddy!
@@rawmath Cool, thanks!
What if the dog is Cerberus and it can fly? 😂✌️
Thanks teacher this actually helped me
What if you used other conjunctions? Don't just use then
In before a mutation makes a 3 headed dog... XD
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If, then
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Great
Thank you, you explained this very well. You made me understand.
This is a superb explanation. It made the topic easier to understand.
this helped me!
Wet happy to hear that 😀
how about this? If 4 < 3, then 7 = 8.
It has no connection but both are false.
lol ok it's obviously true haha i was just sleepy & confused
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