Create logical_and.md (#7640)

* Create logical_and.md

* minor content fixes

* Format fix and fixed the file error

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Author: silentpro-dev

content/pytorch/concepts/tensors/terms/logical-and/logical-and.md

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+---
+Title: '.logical_and()'
+Description: 'Performs an element-wise logical AND operation on two input tensors, returning a tensor of Boolean values.'
+Subjects:
+  - 'Data Science'
+  - 'Machine Learning'
+Tags:
+  - 'Logical'
+  - 'Operators'
+  - 'Python'
+  - 'PyTorch'
+  - 'Tensors'
+CatalogContent:
+  - 'intro-to-py-torch-and-neural-networks'
+  - 'py-torch-for-classification'
+---
+
+The **`torch.logical_and()`** function in PyTorch performs an element-wise logical AND operation between two [tensors](https://www.codecademy.com/resources/docs/pytorch/tensors). It returns a new tensor with boolean values (`True` or `False`) depending on whether the corresponding elements in both input tensors evaluate to `True`.
+
+This operation is often used in tensor-based computations where conditional checks need to be applied element-wise, such as in masking or filtering data.
+
+## Syntax
+
+```pseudo
+torch.logical_and(input, other, *, out=None)
+```
+
+**Parameters:**
+
+- `input` (Tensor): The first tensor for the logical AND operation.
+- `other` (Tensor): The second tensor, must be broadcastable to the shape of `input`.
+- `out` (Tensor, optional): The output tensor to store the result.
+
+**Return value:**
+
+A tensor of type `torch.bool` containing the result of the element-wise logical AND operation.
+
+## Example 1: Basic Usage
+
+In this example, two Boolean tensors are compared element-wise using `torch.logical_and()`:
+
+```py
+import torch
+
+a = torch.tensor([True, False, True])
+b = torch.tensor([True, True, False])
+
+result = torch.logical_and(a, b)
+print(result)
+```
+
+The output of this code is as follows:
+
+```shell
+tensor([True, False, False])
+```
+
+## Example 2: Using with Integer Tensors
+
+In this example, integer tensors are treated as Boolean values, with nonzero as `True` and 0 as `False`:
+
+```py
+import torch
+
+x = torch.tensor([1, 0, 3])
+y = torch.tensor([2, 0, 0])
+
+result = torch.logical_and(x, y)
+print(result)
+```
+
+The output of this code is:
+
+```shell
+tensor([True, False, False])
+```
+
+## Example 3: Broadcasting in `torch.logical_and()`
+
+In this example, [broadcasting](https://pytorch.org/docs/stable/notes/broadcasting.html) allows a smaller tensor to be compared across the rows of a larger tensor.
+
+```py
+import torch
+
+m = torch.tensor([[1, 0], [0, 1]])
+n = torch.tensor([1, 0])
+
+result = torch.logical_and(m, n)
+print(result)
+```
+
+The output of this code will be:
+
+```shell
+tensor([[True, False],
+        [False, False]])
+```