In a classic Piaget’s experiment, A 9-year-old child understands that two glasses of water have the same volume, even though the water line in one glass is taller than the other. This child is demonstrating ___ and is in Piaget’s ___ stage of cognitive development.

4÷12={“version”:”1.1″,”math”:”4÷12=”}

Which of the following is equivalent to 0.4?

67{“version”:”1.1″,”math”:”67″} is 

OPTIONAL BONUS QUESTION (please do this question only after you have completed the others). What was something that you studied for that was not on this exam? Use this opportunity to show me what else you know that this exam did not cover.  It is intended that you be able to upload your work here and use whatever apps you need to do so. However, if you run into any issues doing so with Honorlock, you may email me your work or upload to “assignments”. Be sure that you have clearly labeled everything, and write something in the textbox so that I know (e.g. “I uploaded this problem to D2L and labeled it ‘problem 2 the problem about ____”). 

Determine whether the following two compound propositions are logically equivalent. Show/demonstrate that your answer is correct and explain. p → q {“version”:”1.1″,”math”:”p\rightarrow q “} q → p {“version”:”1.1″,”math”:”q\rightarrow p “} It is intended that you be able to upload your work here and use whatever apps you need to do so. However, if you run into any issues doing so with Honorlock, you may email me your work or upload to “assignments”. Be sure that you have clearly labeled everything, and write something in the textbox so that I know (e.g. “I uploaded this problem to D2L and labeled it ‘problem 2 the problem about ____”). 

Identify the contrapositive of  r → s {“version”:”1.1″,”math”:”r\rightarrow s “}

 Write an expression logically equivalent to the following expression and that doesn’t use the arrow (if-then) symbol. Make your expression as simple as possible. Show all your work.  ¬ ( p → q ) {“version”:”1.1″,”math”:”\neg (p\rightarrow q)”} It is intended that you be able to upload your work here and use whatever apps you need to do so. However, if you run into any issues doing so with Honorlock, you may email me your work or upload to “assignments”. Be sure that you have clearly labeled everything, and write something in the textbox so that I know (e.g. “I uploaded this problem to D2L and labeled it ‘problem 2 the problem about ____”). 

OPTIONAL: If you want the possibility of partial credit for wrong answers to the other question on this page, upload your work or give your rationale here. You are also welcome to upload an audio explanation. Please ensure that any attachment is upright and legible.  For your uploads: please label the file with your name, and some indication of which problem it is (not the problem number, but something about the problem. The problems are shuffled so not everyone has the same number). It is intended that you be able to upload your work here and use whatever apps you need to do so. However, if you run into any issues doing so with Honorlock, you may email me your work or upload to “assignments”. Be sure that you have clearly labeled everything, and write something in the textbox so that I know (e.g. “I uploaded this problem to D2L and labeled it ‘problem 2 the problem about ____”). 

Which of the following are propositions? Assume that Q(x) and R(x) and predicates, and that the domain is the set of positive integers. Select all the apply.