diff --git a/spec/API_specification/elementwise_functions.md b/spec/API_specification/elementwise_functions.md
index 2569a0f6e..8959d2b91 100644
--- a/spec/API_specification/elementwise_functions.md
+++ b/spec/API_specification/elementwise_functions.md
@@ -316,6 +316,30 @@ Calculates the division for each element `x1_i` of the input array `x1` with the
 
 #### Returns
 
+-   **out**: _<array>_
+
+    -   an array containing the element-wise results.
+
+### <a name="equal" href="#equal">#</a> equal(x1, x2, /, *, out=None)
+
+Computes the truth value of `x1_i == x2_i` for each element `x1_i` of the input array `x1` with the respective element `x2_i` of the input array `x2`.
+
+#### Parameters
+
+-   **x1**: _&lt;array&gt;_
+
+    -   first input array.
+
+-   **x2**: _&lt;array&gt;_
+
+    -   second input array. Must be compatible with `x1` (see :ref:`broadcasting`). 
+
+-   **out**:  _Optional\[ &lt;array&gt; ]_
+
+    -   output array. If provided, the output array must be compatible with the provided input arrays (see :ref:`broadcasting`). If not provided or is `None`, an uninitialized return array, whose underlying data type is `bool`, must be created and then filled with the result of each element-wise computation. Default: `None`.
+
+#### Returns
+
 -   **out**: _&lt;array&gt;_
 
     -   an array containing the element-wise results.
@@ -368,6 +392,102 @@ Rounds each element `x_i` of the input array `x` to the greatest (i.e., closest
 
     -   an array containing the rounded result for each element in `x`.
 
+### <a name="greater" href="#greater">#</a> greater(x1, x2, /, *, out=None)
+
+Computes the truth value of `x1_i > x2_i` for each element `x1_i` of the input array `x1` with the respective element `x2_i` of the input array `x2`.
+
+#### Parameters
+
+-   **x1**: _&lt;array&gt;_
+
+    -   first input array.
+
+-   **x2**: _&lt;array&gt;_
+
+    -   second input array. Must be compatible with `x1` (see :ref:`broadcasting`). 
+
+-   **out**:  _Optional\[ &lt;array&gt; ]_
+
+    -   output array. If provided, the output array must be compatible with the provided input arrays (see :ref:`broadcasting`). If not provided or is `None`, an uninitialized return array, whose underlying data type is `bool`, must be created and then filled with the result of each element-wise computation. Default: `None`.
+
+#### Returns
+
+-   **out**: _&lt;array&gt;_
+
+    -   an array containing the element-wise results.
+
+### <a name="greater_equal" href="#greater_equal">#</a> greater_equal(x1, x2, /, *, out=None)
+
+Computes the truth value of `x1_i >= x2_i` for each element `x1_i` of the input array `x1` with the respective element `x2_i` of the input array `x2`.
+
+#### Parameters
+
+-   **x1**: _&lt;array&gt;_
+
+    -   first input array.
+
+-   **x2**: _&lt;array&gt;_
+
+    -   second input array. Must be compatible with `x1` (see :ref:`broadcasting`). 
+
+-   **out**:  _Optional\[ &lt;array&gt; ]_
+
+    -   output array. If provided, the output array must be compatible with the provided input arrays (see :ref:`broadcasting`). If not provided or is `None`, an uninitialized return array, whose underlying data type is `bool`, must be created and then filled with the result of each element-wise computation. Default: `None`.
+
+#### Returns
+
+-   **out**: _&lt;array&gt;_
+
+    -   an array containing the element-wise results.
+
+### <a name="less" href="#less">#</a> less(x1, x2, /, *, out=None)
+
+Computes the truth value of `x1_i < x2_i` for each element `x1_i` of the input array `x1` with the respective element `x2_i` of the input array `x2`.
+
+#### Parameters
+
+-   **x1**: _&lt;array&gt;_
+
+    -   first input array.
+
+-   **x2**: _&lt;array&gt;_
+
+    -   second input array. Must be compatible with `x1` (see :ref:`broadcasting`). 
+
+-   **out**:  _Optional\[ &lt;array&gt; ]_
+
+    -   output array. If provided, the output array must be compatible with the provided input arrays (see :ref:`broadcasting`). If not provided or is `None`, an uninitialized return array, whose underlying data type is `bool`, must be created and then filled with the result of each element-wise computation. Default: `None`.
+
+#### Returns
+
+-   **out**: _&lt;array&gt;_
+
+    -   an array containing the element-wise results.
+
+### <a name="less_equal" href="#less_equal">#</a> less_equal(x1, x2, /, *, out=None)
+
+Computes the truth value of `x1_i <= x2_i` for each element `x1_i` of the input array `x1` with the respective element `x2_i` of the input array `x2`.
+
+#### Parameters
+
+-   **x1**: _&lt;array&gt;_
+
+    -   first input array.
+
+-   **x2**: _&lt;array&gt;_
+
+    -   second input array. Must be compatible with `x1` (see :ref:`broadcasting`). 
+
+-   **out**:  _Optional\[ &lt;array&gt; ]_
+
+    -   output array. If provided, the output array must be compatible with the provided input arrays (see :ref:`broadcasting`). If not provided or is `None`, an uninitialized return array, whose underlying data type is `bool`, must be created and then filled with the result of each element-wise computation. Default: `None`.
+
+#### Returns
+
+-   **out**: _&lt;array&gt;_
+
+    -   an array containing the element-wise results.
+
 ### <a name="log" href="#log">#</a> log(x, /, *, out=None)
 
 Calculates an implementation-dependent approximation to the natural (base `e`) logarithm, having domain `[0, +infinity]` and codomain `[-infinity, +infinity]`, for each element `x_i` of the input array `x`.
@@ -420,6 +540,30 @@ Calculates the product for each element `x1_i` of the input array `x1` with the
 
     -   an array containing the element-wise products.
 
+### <a name="not_equal" href="#not_equal">#</a> not_equal(x1, x2, /, *, out=None)
+
+Computes the truth value of `x1_i != x2_i` for each element `x1_i` of the input array `x1` with the respective element `x2_i` of the input array `x2`.
+
+#### Parameters
+
+-   **x1**: _&lt;array&gt;_
+
+    -   first input array.
+
+-   **x2**: _&lt;array&gt;_
+
+    -   second input array. Must be compatible with `x1` (see :ref:`broadcasting`). 
+
+-   **out**:  _Optional\[ &lt;array&gt; ]_
+
+    -   output array. If provided, the output array must be compatible with the provided input arrays (see :ref:`broadcasting`). If not provided or is `None`, an uninitialized return array, whose underlying data type is `bool`, must be created and then filled with the result of each element-wise computation. Default: `None`.
+
+#### Returns
+
+-   **out**: _&lt;array&gt;_
+
+    -   an array containing the element-wise results.
+
 ### <a name="round" href="#round">#</a> round(x, /, *, out=None)
 
 Rounds each element `x_i` of the input array `x` to the nearest integer-valued number.