Fill in the following derivation. You may use any rule from SD+ or PD+.

Shortcuts:

• To type a universal quantifier, e.g., (^x), or an existential quantifier, like (%y), you can leave out the parentheses. They will be added in after you've moved on to the next field.
• You may use the standard typing shortcuts, i.e., you need not use the shift key to get the computer to know you mean '&', '(', etc.
• Slash shortcuts : For all rules of inference of SL you may type the justification, TAB, then type '/' or '//' and TAB. The answer you intended will likely appear! This will not work for PL rules: we need to learn to do these on our own.
• You may do more than one problem on this page. At any time you would like to start a new problem and give it a name just type "new" into the justification field. You'll be prompted for the rest.

(As always, if you have questions, send me an e-mail at [email protected] or use the course discussion forum.)