symfalse

Create a symbolic inequality $$x^2>4$$.

syms x
eq = x^2 > 4

eq = $$4<x^2$$

Assume that $$-2<x<2$$.

assume(-2<x & x<2)

Simplify the condition represented by the symbolic inequality eq. The simplify function returns the symbolic logical constant symfalse since the condition never holds for the assumption $$-2<x<2$$.

F = simplify(eq)

F = $$\mathrm{symfalse}$$

Display the data type of F, which is sym.

class(F)

ans = 
'sym'

You can also use isAlways to check if the inequality does not hold under the assumption being made. In this example, isAlways returns logical 0 (false).

TF = isAlways(eq)

TF = logical
   0

Use symfalse to generate a 3-by-3 square matrix of symbolic logical symfalses.

F = symfalse(3)

F = 
$$\left(\begin{array}{ccc}\mathrm{symfalse}& \mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}& \mathrm{symfalse}\end{array}\right)$$

Display the data type of T, which is sym.

class(F)

ans = 
'sym'

Next, use symfalse to generate a 3-by-2-by-2 array of symbolic logical symfalses.

F = symfalse(3,2,2)

F(:,:,1) = 
$$\left(\begin{array}{cc}\mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\end{array}\right)$$

F(:,:,2) = 
$$\left(\begin{array}{cc}\mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\end{array}\right)$$

Alternatively, you can use a size vector to specify the size of the array.

F = symfalse([3,2,2])

F(:,:,1) = 
$$\left(\begin{array}{cc}\mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\end{array}\right)$$

F(:,:,2) = 
$$\left(\begin{array}{cc}\mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\end{array}\right)$$

Create a truth table for the and operation applied to the two symbolic logical constants, symtrue and symfalse.

A = [symtrue symfalse]

A = $$\left(\begin{array}{cc}\mathrm{symtrue}& \mathrm{symfalse}\end{array}\right)$$

B = [symtrue; symfalse]

B = 
$$\left(\begin{array}{c}\mathrm{symtrue}\\ \mathrm{symfalse}\end{array}\right)$$

TF = and(A,B)

TF = 
$$\left(\begin{array}{cc}\mathrm{symtrue}& \mathrm{symfalse}\\ \mathrm{symfalse}& \mathrm{symfalse}\end{array}\right)$$

Combine symbolic logical constants with logical operators and, not, or, and xor (or their shortcuts).

TF = xor(symtrue,or(symfalse,symfalse))

TF = $$\mathrm{symtrue}$$

TF = symtrue & ~(symfalse)

TF = $$\mathrm{symtrue}$$

Convert the symbolic logical constant symfalse to a logical value.

T1 = logical(symfalse)

T1 = logical
   0

Convert the symbolic logical constant symfalse to numeric values in double precision and variable precision.

T2 = double(symfalse)

T2 = 
0

T3 = vpa(symfalse)

T3 = $$0.0$$

Show the data types of T1, T2, and T3.

whos

  Name      Size            Bytes  Class      Attributes

  T1        1x1                 1  logical              
  T2        1x1                 8  double               
  T3        1x1                 8  sym