The Fundamental Theorem of World Theory
... are defined as usual. Informally, the three classes of variable range over objects, propositions, and properties, respectively. The actual shapes of these variables are irrelevant; the metavariables x, y, and z (possibly with numerical subscripts) will range over individual variables; likewise p, q, ...
... are defined as usual. Informally, the three classes of variable range over objects, propositions, and properties, respectively. The actual shapes of these variables are irrelevant; the metavariables x, y, and z (possibly with numerical subscripts) will range over individual variables; likewise p, q, ...
Predicate Logic
... If P(x) denotes “x is an undergraduate student” and U is {Enorlled Students in COMPSCI 230}, then x P(x) is TRUE. If P(x) denotes “x > 0” and U is the integers, then x P(x) is FALSE. If P(x) denotes “x > 0” and U is the positive integers, then x P(x) is TRUE. If P(x) denotes “x is even” and U is ...
... If P(x) denotes “x is an undergraduate student” and U is {Enorlled Students in COMPSCI 230}, then x P(x) is TRUE. If P(x) denotes “x > 0” and U is the integers, then x P(x) is FALSE. If P(x) denotes “x > 0” and U is the positive integers, then x P(x) is TRUE. If P(x) denotes “x is even” and U is ...
Lecture01 - Mathematics
... (3) Blue is the best color to paint a house. (This is a matter of opinion, not truth. It may be your favorite color, but it is not objective truth.) (4) Coffee tastes better than tea. (Again, this is a matter of taste, not truth.) (5) The integer n is even. (Since n has no value, this statement is ...
... (3) Blue is the best color to paint a house. (This is a matter of opinion, not truth. It may be your favorite color, but it is not objective truth.) (4) Coffee tastes better than tea. (Again, this is a matter of taste, not truth.) (5) The integer n is even. (Since n has no value, this statement is ...
Exercise
... • Show that if n is an odd integer, there is a unique integer k such that n is the sum of k-2 and k+3. • Prove that there are no solutions in positive integers x and y to the equation 2x2 + 5y2 = 14. • If x3 is irrational then x is irrational • Prove or disprove – if x, y are irrational, x + y is ir ...
... • Show that if n is an odd integer, there is a unique integer k such that n is the sum of k-2 and k+3. • Prove that there are no solutions in positive integers x and y to the equation 2x2 + 5y2 = 14. • If x3 is irrational then x is irrational • Prove or disprove – if x, y are irrational, x + y is ir ...
Document
... between the antecedent or the consequence. The “meaning” of p →q depends only on the truth values of p and q. These implications are perfectly fine, but would not be used in ordinary English. “If the moon is made of green cheese, then I have more ...
... between the antecedent or the consequence. The “meaning” of p →q depends only on the truth values of p and q. These implications are perfectly fine, but would not be used in ordinary English. “If the moon is made of green cheese, then I have more ...
