Biconditional Puns

I see my classmates make this mistake a lot as an undergrad, and it’s always somewhat funny because I know it’s an easy mistake we’ve all made when you’re not being careful.

Most recently I’ve seen this with the divergence test for infinite series — where students assume that because the limit of the general term of an infinite series goes to zero as n goes to infinity, that it must be convergent.

Little confused here, if p and q then the statement is true, if p and q are false then the statement is true, if p is true and q is false then the statement is false. So what if p is false but q is true? Is the statement false or true?

In the program I am currently writing switching these two doesn't cause any errors. Are these same?

Edit: Also or can work too. Am I missing something ?

For example, in English "if and only if" is written as "iff".

Similarly, in Serbian "ako i samo ako" is written as "akko".

To prove "if and only if" statements in mathematics, one must prove the forward and backward directions. Suppose I prove the forward direction line by line. Let's say it starts with Line 1 and ends with Line 10. That's the forward direction. Now, for the backward direction, is there anything wrong with starting with Line 10 and writing the proof in reverse order all the way back to Line 1? Most forward and backward direction proofs have entirely different approaches most times. Can't I just work backwards from one direction to prove the other? Does this method work every time?

Hi there,

Would someone be able to explain the difference, if there is one, between the two biconditional statements?

1. "Ted will be assigned to a group if and only if Steve is"

S<----->T

Does this mean if S is in then T must also be in? Could we also say that if T is in, S must be out?

2. "Either both Sarah and Ryan are on Team A, or they are both not?

1. a → (b ∧ c)
2. ~ (x ∨y)
3. p ∧q ↔ r

https://courses.umass.edu/phil110-gmh/text/c04.pdf

See #16 and #17 in the article. When “unless” is used in the strong sense, that is, when it means “except for”, this indicates the biconditional.

When it is used in the “weak sense” - typically includes the word “not” or “no”, then the logic goes in only one direction.

95% of the time when the LSAT uses the word unless/without, it will include the word “no” or “not”.

Examples:

No deprivation of life, liberty, or property without due process of law.

No warrant shall issue but upon probable cause.

Granted, those two above are from the Bill of Rights, but still good examples.

I feel like I get mixed up when reading a rule, and I don't know if it's a biconditional or a not both rule. What's the difference in verbiage so I can quickly detect between the two?

I'm pretty sure this one is trapezoid but still I really want to be sure as I my grade could use an improvement for sure.

Image: https://imgur.com/a/g4uTdjf

I believe the answer is number 1 however I do really want to make sure. My grade is not doing too hot in this class and I really want to bring it up. Thanks in advance Kind Redditors.

Image: https://imgur.com/a/UxgznW7

Isn't the "if and" part redundant? Wouldn't it be better if the form was "P only if Q"?

For example -- Conditional: If Michigan is playing a close game, they will lose. Converse: If Michigan loses, it was a close game. This is a biconditional because both statements are true.

Additionally, if you can think of true inverses and contrapositives, that would be helpful too.

https://preview.redd.it/134csph05em21.png?width=1012&format=png&auto=webp&s=09e51a4b6ca00218c5a3ac14faa0c599705d0523

https://preview.redd.it/t8ja4qh05em21.png?width=1010&format=png&auto=webp&s=7b86f74b8e7ddda5b3dc3b8e9df1d384be50554f

I thought he said the Biconditional question was due right before the exam, so I believed it was due on Tuesday. I went online just now, and nope it was due today at 12:35pm. The syllabus said that all the questions required on hyperslate must be completed to get a grade; is this true? Or can I afford to miss this one?

Hi there! In class we've been doing truth functional logic derivations. Our textbook is forall x. So we're doing proofs basically. I'm really stuck on one and have no idea where to go with it. Premise: A biconditonal B //// Conclusion: B biconditional A I tried doing disjunction introduction with an A and a B (A biconditional B, OR A, OR, B) and then disjunction elimination to get A, B on their own then biconditonal intro but I'm not sure if that's quite right. Can anyone offer some insight?

I have been studying logic with a friend recently and realize I don't fully understand these two concepts. My first question is why is it that in a truth table for a conditional/biconditional if the hypothesis and conclusion are both false the conditional/biconditional is true? Second how exactly do you determine a valid argument? As far as I understand, it just requires that you have an argument where if all the premises are true then the conclusion must be true. Is there anything else to it?

I'm doing an assingment where I'm supposed to give 15 examples of the four connective symbols regarding prepositions (and, or, implication, biconditional) and their equivalent english conjunctions.

I'm struggling to find the difference between "implication" and "biconditional" (for english conjunctions). For example, "because" is equivalent to "implication" because "The trucker likes driving, because that's his job". because is being used as a cause and effect conjunctions where it explains why the trucker likes driving, but how could I differentiate this with "biconditionals"?

Hi,

I am currently struggling with understanding how to make inferences on the logic games. I can write out the conditional statements and the contrapositive. Then combining them gets tricky and understanding what their implications are for the game.

Any tips?? Videos? Or diagnostic strategies to figure out what I’m missing???

1. a → (b ∧c)
2. ~ (x ∨y)
3. p ∧q ↔r