Problem 1. State whether the following are true or false. If true, give a justifi- cation;...

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Problem 1. State whether the following are true or false. If true, give a justifi- cation; if false, give a counterexample. Here a, b are terms, A, B are designators, and x, y are variables. (a) If B occurs in A, then every occurrence of y in B which is free in A is also free in B. (b) If y does not occur in A, then x is substitutible for y in A[a]. (c) If y occurs in a, then every occurrence of y in A [a] which is not present in A is a free occurrence. (d) If b is substitutible for y in A, then b is substitutible for y in A,[a]. (e) If b is substitutible for y in A, fa], then a, [b] is substitutible for x in A and (A, [a]),[b] = A,a,[b]]. %3| Problem 1. State whether the following are true or false. If true, give a justifi- cation; if false, give a counterexample. Here a, b are terms, A, B are designators, and x, y are variables. (a) If B occurs in A, then every occurrence of y in B which is free in A is also free in B. (b) If y does not occur in A, then x is substitutible for y in A[a]. (c) If y occurs in a, then every occurrence of y in A [a] which is not present in A is a free occurrence. (d) If b is substitutible for y in A, then b is substitutible for y in A,[a]. (e) If b is substitutible for y in A, fa], then a, [b] is substitutible for x in A and (A, [a]),[b] = A,a,[b]]. %3|