3. At Least One

If M is not selected, then T must be chosen. You can then take the contrapositive: If T is not selected, then M must do it.

At The Office Video Summary

“If NOT A → B” means that at least one of A and B (or both). For example:

If Matt is not in the office tomorrow, then Tim must be there.

Diagram this as: ~M → T.

Its contrapositive is:

If Tim is not in the office tomorrow, then Matt must be there.

Diagram this as: ~T → M.

These statements mean that at least one of Matt or Tim must be in the office tomorrow, but they can also both be there.

IF NOT M →  T

Premise #1

If Matt is not in the office (M), then Tim is (T).

~M → T

Premise #2

If Tim is not in the office (T), then Matt is (M).

~T → M

Note: This is the contrapositive of premise 1.

Conclusion

At least Tim (T) or Matt must be at the office (M).

IF NOT T → M

Note: There’s nothing ruling out T and M being together.

Premise #1

If you will not attend the school trip (AST), then you must write a book report (WBR).

~AST → WBR

Premise #2

If you will not write a book report (WBR), then you must attend the school trip (AST).

~WBR → AST

Note: This is the contrapositive of premise 1.

Conclusion

You must at least attend the school trip (AST) or write a book report (WBR).

IF NOT AST → WBR

Note: You can do both the AST and the WBR.

Next LSAT: Sep 08/ Sep 09

Premise #1

If you did not apply to a graduate program at the University of Oxford (O), then you should apply at the University of Cambridge (C).

~O → C

Premise #2

Contrapositive of #1:
If you did not apply for a graduate program at the University of Cambridge (C), then you should apply at the University of Oxford (O).

~C → O

Conclusion

You should apply for a graduate program at least at the University of Oxford (O) or the University of Cambridge (C).

IF NOT O → C

Premise #1

If I will not buy this red shirt (R), then I will buy this blue shirt (B).

~R → B

Premise #2

Contrapositive of #1:
If I will not buy this blue shirt (B), then I will buy this red shirt (R).

~B → R

Conclusion

I will buy at least the red shirt (R) or the blue shirt (B).

IF NOT R → B

Premise #1

If she cannot go to work today (W), then she must attend tomorrow’s meeting (M).

~W → M

Premise #2

Contrapositive of #1:
If she cannot attend tomorrow’s meeting (M), then she must go to work today (W).

~M → W

Conclusion

She must at least go to work today (W) or attend tomorrow’s meeting (M).

IF NOT W → M

Truth Tables

Negation Truth Table

P ~P
 True False
False True

Conjunction ``And`` Truth Table

P Q P and Q
True True True
True False False
False True False
False False False

Conjunction ``Or`` Truth Table

P Q P or Q
True True True
True False True
False True True
False False False

Table Guide

Statement

Symbols

Description
1. If Matt is not in the office tomorrow, then Tim must be there.

~M → T

Given
2. If Tim is not in the office tomorrow, then Matt must be there.

~T → M

Given
3. At least one of Matt or Tim must be in the office tomorrow.

IF NOT M → T

Valid, Combine the 2 premises

Start game

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At Least One

Adaptive

Directions

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  3. To highlight content, highlight it with your cursor and then click the "crayon" icons.
  4. Press the explanation button to view all the question explanations. Scroll through the buttons to view the different questions.
  5. You can flag questions.

Instructions

This is an adaptive drill: The questions will get harder or easier depending on your performance. You can't go backwards or change prior answers.

  1. Flag a question.
  2. Mark text.
  3. Eliminate choice.
  4. Fullscreen.
  5. Delete data and redo.

Complete: 0 / 3 correct

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Score Report

Question 3
00:00 / 00:00
Adj 30

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Now that we learned how to combine statements, we can do more complex deductions, such as If and Only If.

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