# Tree Predicate Exercises: Roll your own

Logical System
###### 6/3/12

You can try your own exercises here.

Here are a few hints

• You have to use the right (unicode/html) logical symbols. Check Writing symbols
• The symbols in use here are ~ & ∨ →

∀ ∃ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ (so copy and paste or drag and drop these). In the syntax we prefer that the quantifers do not have brackets around them so a quantified formula might look like ∀x(A(x)→B(x,x)). Notice that the 'arguments' to a predicate have brackets around them, and if the arguments are a list they will be separated by commas. You can use proper subscripts (shown above) on variables (or constants or predicates). For example, ∀x₁(A(x₁)→B(x₁,x₁)).
• When entering from a selection, the software will take a single formula (say, A) or a comma separated list of formulas (say, A,B,C) or a possibly empty comma separated list of formulas followed by ∴ and another formula (say, A,B,C ∴ D). In the last case it will load the negation of the conclusion.
• Just type, cut and paste, or drag and drop, whatever you wish, into the lower text box. Then make a selection and hit the Start button.
• The iPad, and similar, keyboards have a little trick that might catch you out. If you type a single letter, say 'a', they will automatically put it in upper case to 'A' because they assume you are starting a sentence. But, actually, if you are instantiating a quantifier you have to use lower case.