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PROOF.H
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PROOF.H
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void commanproof(int col,int row,char name[]);
void endproof(void);
void xbar(int col,int row);
void ybar(int col,int row);
void xbar1(int col,int row);
void ybar1(int col,int row);
void negation(void)
{
commanproof(100,6,"Involation Laws");
setcolor(15);
line(getmaxx()/2,75,getmaxx()/2,getmaxy()-75);
line(15,getmaxy()-75,getmaxx()-15,getmaxy()-75);
setcolor(1);
settextstyle(1,0,2);
outtextxy(280,150,"X = X");line(280,153,292,153);line(280,150,292,150);
setcolor(0);
settextstyle(2,0,6);
outtextxy(250,190,"e.g X = 1");
outtextxy(240,230,"L.H.S 1 = 0");
line(320,231,328,231);line(320,228,328,228);line(360,231,370,231);
outtextxy(240,270," 1 = X");
outtextxy(250,330,"Hence Proved.");
setcursorpos(x,y);
cursoron();
endproof();
}
void complementory(void)
{
commanproof(50,6,"Complementory Laws");
setcolor(1);
settextstyle(1,0,2);
outtextxy(42,90,"a) X + = 1");xbar1(162,90);
outtextxy(342,90,"b) X . = 0");xbar1(455,90);
setcolor(0);
settextstyle(2,0,6);
// proof of a part.
outtextxy(72,140,"e.g X = 1 then = 0");xbar(225,140);
outtextxy(42,180,"L.H.S 1 + 0 = 1");
outtextxy(100,220,"L.H.S = R.H.S");
// proof of b part.
outtextxy(372,140,"e.g X = 1 then = 0");xbar(525,140);
outtextxy(342,180,"L.H.S 1 . 0 = 0");
outtextxy(400,220,"L.H.S = R.H.S");
setcursorpos(x,y);
cursoron();
endproof();
}
void demorgan(void)
{
commanproof(100,6,"De Morgan's Laws");
setcolor(1);
settextstyle(1,0,2);
outtextxy(42,90,"a) X + Y = ");line(95,90,160,90);
xbar1(210,90);ybar1(260,90);outtextxy(240,90,".");
outtextxy(342,90,"b) X . Y = ");line(400,90,450,90);
xbar1(510,90);ybar1(570,90);outtextxy(540,90,"+");
setcolor(0);
settextstyle(2,0,6);
// proof of a part.
outtextxy(72,140,"e.g X = 1 and Y = 0");
outtextxy(42,180,"L.H.S 1 + 0 = 1 = 0");
line(125,180,170,180);line(202,180,210,180);
xbar(115,220);ybar(218,220);
outtextxy(135,220,"= 0 and");outtextxy(238,220,"= 1");
outtextxy(42,260,"R.H.S 0 . 1 = 0");
outtextxy(100,300,"L.H.S = R.H.S");
// proof of b part.
outtextxy(372,140,"e.g X = 1 and Y = 0");
outtextxy(342,180,"L.H.S 1 . 0 = 0 = 1");
line(425,180,467,180);line(499,180,507,180);
xbar(415,220);ybar(518,220);
outtextxy(435,220,"= 0 and");outtextxy(538,220,"= 1");
outtextxy(342,260,"R.H.S 0 + 1 = 1");
outtextxy(400,300,"L.H.S = R.H.S");
setcursorpos(x,y);
cursoron();
endproof();
}
void associative(void)
{
commanproof(100,6,"Associative Laws");
setcolor(15);
line(getmaxx()/2,75,getmaxx()/2,getmaxy()-75);
line(15,getmaxy()-75,getmaxx()-15,getmaxy()-75);
setcolor(1);
settextstyle(1,0,2);
outtextxy(42,90,"a) X + ( Y + Z ) = ( X + Y ) + Z = X + Y + Z");
outtextxy(42,220,"b) X . ( Y . Z ) = ( X . Y ) . Z = X . Y . Z");
setcolor(0);
settextstyle(2,0,6);
// proof of a part.
outtextxy(92,140,"In this case only open the Bracketes.");
outtextxy(125,180,"X + Y + Z = X + Y + Z = X + Y + Z");
// proof of b part.
outtextxy(92,260,"In this case only open the Bracketes.");
outtextxy(125,300,"X . Y . Z = X . Y . Z = X . Y . Z");
setcursorpos(x,y);
cursoron();
endproof();
}
void absorption(void)
{
commanproof(100,6,"Absorption Laws");
setcolor(1);
settextstyle(1,0,2);
outtextxy(42,90,"a) X . ( X + Y ) = X");
outtextxy(342,90,"b) X + ( X . Y ) = X");
setcolor(0);
settextstyle(2,0,6);
// proof of a part.
outtextxy(92,140,"X . X + X . Y = X");
outtextxy(92,180,"X + X . Y = X (X.X=X)");
outtextxy(102,220,"X ( 1 + Y ) = X");
outtextxy(105,260,"X . 1 = X (1+Y=1)");
outtextxy(135,300,"X = X");
// proof of b part.
outtextxy(392,140,"X + X . Y = X");
outtextxy(388,180,"X ( 1 + Y ) = X");
outtextxy(398,220,"X . 1 = X (1+Y=1)");
outtextxy(415,260,"X = X");
setcursorpos(x,y);
cursoron();
endproof();
}
void properties(void)
{
commanproof(40,6,"Properties of 0 and 1");
setcolor(1);
settextstyle(1,0,2);
outtextxy(42,90,"a) X + 1 = 1");
outtextxy(342,90,"b) X . 0 = 0");
setcolor(0);
settextstyle(2,0,6);
// proof of a part.
outtextxy(62,140,"(X + 1) . 1 = 1 (X.1=X)");
outtextxy(62,180,"(X + 1).(X + ) = 1 (X+ =1)");
xbar(172,180);xbar(278,180);
outtextxy(82,220,"X + 1 . = 1");
xbar(153,220);
outtextxy(75,250,"X + = 1 (1. = )");
xbar(115,250);xbar(267,250);xbar(290,250);
outtextxy(95,280,"1 = 1 (X+ =1)");
xbar(273,280);
// proof of b part.
outtextxy(362,140,"X . 0 + 0 = 0 (X+0=X)");
outtextxy(362,180,"X . 0 + X . = 0 (X. =0)");
xbar(468,180);xbar(567,180);
outtextxy(382,220,"X ( 0 + ) = 0");
xbar(461,220);
outtextxy(375,250,"X . = 0 (0+ = )");
xbar(415,250);xbar(567,250);xbar(588,250);
outtextxy(405,280,"0 = 0 (X. =0)");
xbar(570,280);
setcursorpos(x,y);
cursoron();
endproof();
}
void idempotent(void)
{
commanproof(90,6,"Idempotent Laws");
setcolor(1);
settextstyle(1,0,2);
outtextxy(42,90,"a) X + X = X");
outtextxy(342,90,"b) X . X = X");
setcolor(0);
settextstyle(2,0,6);
// proof of a part.
outtextxy(62,140,"(X + X) . 1 = X (X.1=X)");
outtextxy(62,180,"(X + X).(X + ) = X (X+ =1)");
xbar(172,180);xbar(278,180);
outtextxy(82,220,"X + X . = X");
xbar(153,220);
outtextxy(75,250,"X + 0 = X (X. =0)");
xbar(267,250);
outtextxy(95,280,"X = X (X+0=X)");
// proof of b part.
outtextxy(362,140,"X . X + 0 = X (X+0=X)");
outtextxy(362,180,"X . X + X . = X (X. =0)");
xbar(468,180);xbar(567,180);
outtextxy(382,220,"X ( X + ) = X");
xbar(461,220);
outtextxy(375,250,"X . 1 = X (X+ =1)");
xbar(567,250);
outtextxy(405,280,"X = X (X.1=X)");
setcursorpos(x,y);
cursoron();
endproof();
}
void distributive(void)
{
commanproof(80,6,"Distributive Laws");
setcolor(1);
settextstyle(1,0,2);
outtextxy(35,90,"a) X+(Y.Z) = (X+Y).(X+Z)");
outtextxy(342,90,"b) X.(Y+Z) = X.Y + X.Z");
setcolor(0);
settextstyle(2,0,6);
// proof of a part.
outtextxy(62,140,"e.g X=1, Y=2 and Z=3");
outtextxy(40,170,"Put the values in this eq.");
outtextxy(62,220,"1 + (2.3) = (1 + 2).(1 + 3)");
outtextxy(112,250,"1 + 6 = 3 . 4");
outtextxy(152,280,"7 = 7");
// proof of b part.
outtextxy(362,140,"e.g X=1, Y=2 and Z=3");
outtextxy(342,170,"Put the values in this eq.");
outtextxy(360,220,"1 . (2 + 3) = 1 . 2 + 1 . 3");
outtextxy(415,250,"1 . 5 = 2 + 3");
outtextxy(450,280,"5 = 5");
setcursorpos(x,y);
cursoron();
endproof();
}
void commutative(void)
{
commanproof(62,6,"Commutative Laws");
setcolor(1);
settextstyle(1,0,2);
outtextxy(42,90,"a) X + Y = Y + X");
outtextxy(342,90,"b) X . Y = Y . X");
setcolor(0);
settextstyle(2,0,6);
// proof of a part.
outtextxy(72,140,"e.g X = 1 and Y = 2");
outtextxy(40,170,"Put the values in this eq.");
outtextxy(112,200,"1 + 2 = 2 + 1");
outtextxy(152,250,"3 = 3");
// proof of b part.
outtextxy(372,140,"e.g X = 1 and Y = 2");
outtextxy(342,170,"Put the values in this eq.");
outtextxy(412,200,"1 . 2 = 2 . 1");
outtextxy(452,250,"2 = 2");
setcursorpos(x,y);
cursoron();
endproof();
}
void identity(void)
{
commanproof(132,6,"Identity Laws");
setcolor(1);
settextstyle(1,0,2);
outtextxy(42,90,"a) X + 0 = X");
outtextxy(342,90,"b) X . 1 = X");
setcolor(0);
settextstyle(2,0,6);
// proof of a part.
outtextxy(72,140,"X + X. = X ( 0=X. )");
xbar(130,140);
xbar(290,140);
outtextxy(72,180,"X (1 + ) = X");
xbar(135,180);
outtextxy(72,220,"X . 1 = X ( X+1=1 )");
outtextxy(132,260,"X = X");
// proof of b part.
outtextxy(372,140,"X.( X + ) = X ( X+ =1 )");
xbar(440,140);
xbar(570,140);
outtextxy(372,180,"X.X + X. = X");
xbar(445,180);
outtextxy(362,220,"X + 0 = X (X.X=X) (X. = 0)");
xbar(568,220);
outtextxy(432,260,"X = X");
setcursorpos(x,y);
cursoron();
endproof();
}
void commanproof(int col,int row,char name[])
{
comman3(0, 0, getmaxx(), getmaxy(), 11);
comman(0, 0, getmaxx(), 75,9);
settextstyle(TRIPLEX_FONT, HORIZ_DIR, 6);
setcolor(0);
outtextxy(col,row,name);
outtextxy(col+1,row+1,name);
setcolor(14);
outtextxy(col-1,row-2,name);
outtextxy(col-2,row-2,name);
comman3(15,76,getmaxx()-15,getmaxy()-15,15);
line(getmaxx()/2,75,getmaxx()/2,getmaxy()-75);
line(15,getmaxy()-75,getmaxx()-15,getmaxy()-75);
comman(270,420,370,450,7);
settextstyle(1,0,4);
outtextxy(300,415,"Ok");
}
void endproof(void)
{
int iop=0,flag=0;
int button;
while (iop != 1)
{
button=getcursorpos(&x,&y);
if (button)
{
flag=1;
if (x >= 270 && x <= 370 && y >= 420 && y <= 450)
{
press1(270,420,370,450);
}
}
if ((!button)&&(flag))
{
flag=0;
press2(270,420,370,450);
delay(150);
if (x >= 270 && x <= 370 && y >= 420 && y <= 450)
{
sound();
iop=1;
cursoroff();
}
}
}
}
void xbar(int col,int row)
{
outtextxy(col,row,"X");
outtextxy(col,row-10,"-");
}
void ybar(int col,int row)
{
outtextxy(col,row,"Y");
outtextxy(col,row-10,"-");
}
void xbar1(int col,int row)
{
outtextxy(col,row,"X");
outtextxy(col+1,row-12,"-");
}
void ybar1(int col,int row)
{
outtextxy(col,row,"Y");
outtextxy(col+1,row-12,"-");
}