elias001
- 359
- 24
- TL;DR Summary
- Quantifier rules of inferences questions in the proof of ##\cap_{i\in \cup F}A_i=\cap_{x\in F}(\cap_{i\in X}A_i)##?
The screenshots below are taken from the 2nd editon of the book How to Prove it A structured approach By: Daniel Velleman and and 3rd edition of the book's solution manual. (Page 5)
The question on page 4 exercise 5b corresponds to the solution in page 5 exercise 6b
Page 1
Page 2
Page 3
Page 4
Page 5
Questions
In the above screenshots, pages one to three lists the inference rules for proving with universal quantifier. But for the exercise 5b in screenshot page 4, the solution exercise 6b shown on page 5 in that screenshot where it says:
Is the author using using universal instantiation for both ##X## and ##i##?
The question on page 4 exercise 5b corresponds to the solution in page 5 exercise 6b
Page 1
Page 2
Page 3
Page 4
Page 5
Questions
In the above screenshots, pages one to three lists the inference rules for proving with universal quantifier. But for the exercise 5b in screenshot page 4, the solution exercise 6b shown on page 5 in that screenshot where it says:
Let ##X\in F## be arbitrary. ##i\in X## be arbitrary.
Is the author using using universal instantiation for both ##X## and ##i##?