With the aid truth tables prove that each of the conditional statements in the image below is a tautology

3. Construct a truth table of (p → ~q) +r

Consider the open statement P(t) which says (∃x)(tx = 20).  Find the full truth set for P if the universal set is R.

Use ONLY the laws of logic and propositional equivalence (see your cheat sheet), to prove that - (p → 9) → ¬9 is a tautology

Determine whether the following proposition is a tautology:(¬p∨¬(r⟶q))⟷(p⟶(¬q∧r)).  can i get a non handwritig answer please so it would be easy to copy

Express the following proposition in a symbolic form by defining atomic propositions and construct truth table for the expression. "If you submit all assessments and sit the final exam then you have more chance to pass this course”. Is it tautology, contradiction or neither?

Show work please

The rule of inference that permits us to derive a specific instance from a universal statement is  A.Existential Generalization.B. Existential Instantiation.C. Universal Generalization.D. Universal Instantiation.

Determine whether the logical statement is a tautology, a contradiction or neither: (p→q) → (p v q). [Hint: Use a truth table with 4 rows; you need to check the last row; all T is a tautology: all F is a contradition; a mixture of T and F is neither.] Example statement: If adopting new software leads to savings, then we'll either adopt new software or save money. The parentheses fit in the statement like this: If (adopting new software leads to savings), then (we'll either adopt new software or save money). This interpretation gives adopting new software leads to savings = If we adopt new software, then we'll save money O a. Tautology O b. Neither Oc. Contradiction

Using relational predicates ( e.g. F(s,m) for, say, s can fool m), translate the following sentences into predicate logic. You can use English words for the quantification symbols (such as For All x instead of v x) if necessary Also give the negatives of each sentence in English. a) Everybody can fool somebody b) There is no-one who can fool everyone. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).