Line 27: |
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| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | x + y
| + | a + b |
| & = & | | & = & |
− | \texttt{(} x, y \texttt{)} | + | \texttt{(} a, b \texttt{)} |
| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | x + y + z
| + | a + b + c |
| & = & | | & = & |
− | \texttt{((} x, y \texttt{)}, z \texttt{)} | + | \texttt{((} a, b \texttt{)}, c \texttt{)} |
| & = & | | & = & |
− | \texttt{(} x, \texttt{(} y, z \texttt{))} | + | \texttt{(} a, \texttt{(} b, c \texttt{))} |
| \end{matrix}</math> | | \end{matrix}</math> |
| |} | | |} |
| | | |
− | It is important to note that the last expressions are not equivalent to the triple bracket <math>\texttt{(} x, y, z \texttt{)}.</math> | + | It is important to note that the last expressions are not equivalent to the triple bracket <math>\texttt{(} a, b, c \texttt{)}.</math> |
| | | |
| <br> | | <br> |
Line 61: |
Line 61: |
| | <math>0\!</math> | | | <math>0\!</math> |
| |- | | |- |
− | | <math>x\!</math> | + | | <math>a\!</math> |
− | | <math>x\!</math> | + | | <math>a\!</math> |
− | | <math>x\!</math> | + | | <math>a\!</math> |
| |- | | |- |
− | | <math>(x)\!</math> | + | | <math>(a)\!</math> |
− | | <math>\operatorname{Not}\ x</math> | + | | <math>\operatorname{Not}\ a</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | x' \\
| + | a' \\ |
− | \tilde{x} \\ | + | \tilde{a} \\ |
− | \lnot x \\ | + | \lnot a \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
− | | <math>x\ y\ z</math> | + | | <math>a\ b\ c</math> |
− | | <math>x\ \operatorname{and}\ y\ \operatorname{and}\ z</math> | + | | <math>a\ \operatorname{and}\ b\ \operatorname{and}\ c</math> |
− | | <math>x \land y \land z</math> | + | | <math>a \land b \land c</math> |
| |- | | |- |
− | | <math>((x)(y)(z))\!</math> | + | | <math>((a)(b)(c))\!</math> |
− | | <math>x\ \operatorname{or}\ y\ \operatorname{or}\ z</math> | + | | <math>a\ \operatorname{or}\ b\ \operatorname{or}\ c</math> |
− | | <math>x \lor y \lor z</math> | + | | <math>a \lor b \lor c</math> |
| |- | | |- |
− | | <math>(x\ (y))\!</math> | + | | <math>(a\ (b))\!</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | x\ \operatorname{implies}\ y \\
| + | a\ \operatorname{implies}\ b \\ |
− | \operatorname{If}\ x\ \operatorname{then}\ y \\ | + | \operatorname{If}\ a\ \operatorname{then}\ b \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
− | | <math>x \Rightarrow y\!</math> | + | | <math>a \Rightarrow b\!</math> |
| |- | | |- |
− | | <math>(x, y)\!</math> | + | | <math>(a, b)\!</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | x\ \operatorname{not~equal~to}\ y \\
| + | a\ \operatorname{not~equal~to}\ b \\ |
− | x\ \operatorname{exclusive~or}\ y \\
| + | a\ \operatorname{exclusive~or}\ b \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | x \neq y \\
| + | a \neq b \\ |
− | x + y \\
| + | a + b \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
− | | <math>((x, y))\!</math> | + | | <math>((a, b))\!</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | x\ \operatorname{is~equal~to}\ y \\
| + | a\ \operatorname{is~equal~to}\ b \\ |
− | x\ \operatorname{if~and~only~if}\ y \\
| + | a\ \operatorname{if~and~only~if}\ b \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | x = y \\
| + | a = b \\ |
− | x \Leftrightarrow y \\
| + | a \Leftrightarrow b \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
− | | <math>(x, y, z)\!</math> | + | | <math>(a, b, c)\!</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
| \operatorname{Just~one~of} \\ | | \operatorname{Just~one~of} \\ |
− | x, y, z \\
| + | a, b, c \\ |
| \operatorname{is~false}. \\ | | \operatorname{is~false}. \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | x'y~z~ & \lor \\
| + | a'b~c~ & \lor \\ |
− | x~y'z~ & \lor \\
| + | a~b'c~ & \lor \\ |
− | x~y~z' & \\
| + | a~b~c' & \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
− | | <math>((x),(y),(z))\!</math> | + | | <math>((a),(b),(c))\!</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
| \operatorname{Just~one~of} \\ | | \operatorname{Just~one~of} \\ |
− | x, y, z \\
| + | a, b, c \\ |
| \operatorname{is~true}. \\ | | \operatorname{is~true}. \\ |
| & \\ | | & \\ |
| \operatorname{Partition~all} \\ | | \operatorname{Partition~all} \\ |
− | \operatorname{into}\ x, y, z. \\ | + | \operatorname{into}\ a, b, c. \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | x~y'z' & \lor \\
| + | a~b'c' & \lor \\ |
− | x'y~z' & \lor \\
| + | a'b~c' & \lor \\ |
− | x'y'z~ & \\
| + | a'b'c~ & \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | ((x, y), z) \\ | + | ((a, b), c) \\ |
| & \\ | | & \\ |
− | (x, (y, z)) \\ | + | (a, (b, c)) \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
| \operatorname{Oddly~many~of} \\ | | \operatorname{Oddly~many~of} \\ |
− | x, y, z \\
| + | a, b, c \\ |
| \operatorname{are~true}. \\ | | \operatorname{are~true}. \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
− | <p><math>x + y + z\!</math></p> | + | <p><math>a + b + c\!</math></p> |
| <br> | | <br> |
| <p><math>\begin{matrix} | | <p><math>\begin{matrix} |
− | x~y~z~ & \lor \\
| + | a~b~c~ & \lor \\ |
− | x~y'z' & \lor \\
| + | a~b'c' & \lor \\ |
− | x'y~z' & \lor \\
| + | a'b~c' & \lor \\ |
− | x'y'z~ & \\
| + | a'b'c~ & \\ |
| \end{matrix}</math></p> | | \end{matrix}</math></p> |
| |- | | |- |
− | | <math>(w, (x),(y),(z))\!</math> | + | | <math>(x, (a),(b),(c))\!</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | \operatorname{Partition}\ w \\ | + | \operatorname{Partition}\ x \\ |
− | \operatorname{into}\ x, y, z. \\ | + | \operatorname{into}\ a, b, c. \\ |
| & \\ | | & \\ |
− | \operatorname{Genus}\ w\ \operatorname{comprises} \\ | + | \operatorname{Genus}\ x\ \operatorname{comprises} \\ |
− | \operatorname{species}\ x, y, z. \\ | + | \operatorname{species}\ a, b, c. \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | w'x'y'z' & \lor \\
| + | x'a'b'c' & \lor \\ |
− | w~x~y'z' & \lor \\
| + | x~a~b'c' & \lor \\ |
− | w~x'y~z' & \lor \\
| + | x~a'b~c' & \lor \\ |
− | w~x'y'z~ & \\
| + | x~a'b'c~ & \\ |
| \end{matrix}</math> | | \end{matrix}</math> |
| |} | | |} |